Accounting for dust aerosol size distribution in ... - Wiley Online Library

Journal of Geophysical Research: Atmospheres RESEARCH ARTICLE 10.1002/2015JD023078 Key Points: • The benchmark aerosol radiative forcing should be based on size bin results • The skewness is another factor to determine the size distribution • The results from gamma size distribution is more close to observation

Correspondence to: J. Li, [email protected]

Citation: Li, J., Q. Min, Y. Peng, Z. Sun, and J.-Q. Zhao (2015), Accounting for dust aerosol size distribution in radiative transfer, J. Geophys. Res. Atmos., 120, 6537–6550, doi:10.1002/2015JD023078.

Received 7 JAN 2015 Accepted 23 MAY 2015 Accepted article online 29 MAY 2015 Published online 6 JUL 2015

The copyright line for this article was changed on 31 JUL 2015 after original online publication.

Accounting for dust aerosol size distribution in radiative transfer Jiangnan Li1 , Qilong Min2 , Yiran Peng3 , Zhian Sun4 , and Jian-Qi Zhao5 1 Canadian Centre For Climate Modelling and Analysis, Science and Technology Branch, Environment Canada, Victoria, British Columbia, Canada, 2 Atmospheric Sciences Research Center, State University of New York at Albany, Albany, New York, USA, 3 Center for Earth System Science, Tsinghua University, Beijing, China, 4 Centre for Australian Weather and Climate Research, Australian Bureau of Meteorology, Melbourne, Victoria, Australia, 5 Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, China

Abstract The impact of size distribution of mineral dust aerosol on radiative transfer was investigated using the Aerosol Robotic Network-retrieved aerosol size distributions. Three methods for determining the aerosol optical properties using size distributions were discussed. The first is referred to as a bin method in which the aerosol optical properties are determined for each bin of the size distribution. The second is named as an assembly mean method in which the aerosol optical properties are determined with an integration of the aerosol optical parameters over the observed size distribution. The third is a normal parameterization method based on an assumed size distribution. The bin method was used to generate the benchmark results in the radiation calculations against the methods of the assembly mean, and parameterizations based on two size distribution functions, namely, lognormal and gamma were examined. It is seen that the assembly mean method can produce aerosol radiative forcing with accuracy of better than 1%. The accuracies of the parameterizations based on lognormal and gamma size distributions are about 25% and 5%, respectively. Both the lognormal and gamma size distributions can be determined by two parameters, the effective radius and effective variance. The better results from the gamma size distribution can be explained by a third parameter of skewness which is found to be useful for judging how close the assumed distribution is to the observation result. The parameterizations based on the two assumed size distributions are also evaluated in a climate model. The results show that the reflected solar fluxes over the desert areas determined by the scheme based on the gamma size distribution are about 1 W m−2 less than those from the scheme based on the lognormal size distribution, bringing the model results closer to the observations.

1. Introduction Anthropogenic and natural aerosols are recognized as significant atmospheric constituents that affect climate changes. One of the important aerosol properties is the aerosol particle size distribution. According to the observations from the AERONET (Aerosol Robotic Network) [Holben et al., 1998; Huneeus et al., 2011], aerosols observed worldwide present many types of size distribution.

©2015. Her Majesty the Queen in Right of Canada. Reproduced with the permission of the Minister of Environment of Canada. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

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In the early generations of climate models, the aerosol size distribution was not properly represented. Generally, a two-mode scheme was used [Hess et al., 1998; Kinne et al., 2006], which separated the aerosol size distribution into two categories, accumulation mode and coarse mode. Nowadays, more and more climate models are able to simulate the full aerosol size distribution through coupling the atmospheric model with the chemical transport model [Grell et al., 2005; Fast et al., 2006; Gong et al., 2012]. The bin method is one of the typical approaches, where the aerosol size distribution is divided into many bins. The aerosol optical properties can be determined in each bin, and in principle the radiative transfer calculation should be applied to each bin too. However, this is not affordable since radiation is one of the most time-consuming processes in climate models. Therefore, the parameterization method has been proposed, which deals with the aerosol size distribution as a mean of size spectrum, and the individual radiation calculation for each bin can be avoided. In an aerosol optical property parameterization, the aerosol size distribution is usually assumed to be the lognormal size distribution [Kiehl et al., 2000; Li et al., 2001; Kinne et al., 2006], which can be determined by the effective radius, reff , and effective variance, veff . The aerosol optical properties are precalculated for various DUST SIZE DISTRIBUTION FOR RADIATION

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values of reff and veff , and all the precalculated results are stored in a look-up table. For any pair of reff and veff produced in a climate model, the aerosol optical properties can be obtained by an interpolation based on the look-up table. However, the accuracy of this kind of parameterization is seldom investigated. In our opinion, attention should be paid on following issues. First, what should be the benchmark result for the comparison of aerosol optical property parameterization? In previous aerosol parameterization studies, the validation was usually performed by a comparison of aerosol optical properties determined by the parameterization and the exact Mie calculation, but both were based on the same assumed lognormal distribution. There has been no effort to compare the aerosol optical parameterization against the benchmark result based on the true aerosol size distribution. Second, in a parameterization, how accurate is the assumed lognormal size distribution in simulation of the observed shapes of particle size distribution? The lognormal size distribution is a two-parameter scheme and its shape is fully determined by reff and veff , while the observed aerosol size distributions always present complicated shapes. Third, is there any other assumed size distribution better than the lognormal size distribution for simulation of aerosol radiative forcing? To investigate the validity of aerosol optical property parameterization in climate models was the purpose of the study. Here we only focus on dust aerosol, but the methods proposed in this study can be used to check other types of aerosol. In the following section, the dust particle size distributions were discussed based on AERONET observations. In section 3, three methods are proposed for the calculation of dust radiative forcing. The accuracy comparisons for different methods in an offline radiation model and the general circulation model (GCM) are shown in section 4. The conclusions are listed in section 4.

2. Dust Size Distribution Many observations over the globe have shown that the size distributions of aerosol exhibit a continuous and multimode pattern [Holben et al., 1998; Dubovik and King, 2000; Huneeus et al., 2011]. Here we chose mineral dust as a sample, since unlike most of the other aerosols, the hygroscopic effect of soil dust is very weak, which enables us to focus on the effects of particle size distribution. In addition, the geographical distribution of the mineral dust was very uneven with large emission sources in Africa, Middle East, and eastern Asia. We study the aerosol volume-size distributions from the selected 24 “dusty” sites from AERONET (Aerosol Robotic Network) inversion retrieval data. Dusty sites are defined in Huneeus et al. [2011], where the observed monthly mean total aerosol optical depth is larger than 0.2 and the monthly averaged Ångström exponent (AE) is smaller than 0.4 for at least 2 months in a year. In the dusty areas, the dust aerosols have little chance to internally mix with other types of aerosol before they transport through polluted regions or urban areas [DallÓsto et al., 2010]. In Figure 1 the locations of the 24 AERONET sites are shown. There are nine sites in Africa (numbers 1–9, in yellow color), six sites in the Middle East (10–15, in red), seven sites in the Caribbean-America (16–22, in blue), and two other sites in the other parts of the world (23–24, in purple). We do not choose the sites over East Asia, since East Asian sites neither have data record during that time period nor meet the dusty condition. In Figure 2, the vertically integrated aerosol volume-size distributions were plotted for the 24 selected AERONET sites. The AERONET collects ground-based remote sensing data globally [Holben et al., 1998, 2001]. Sun photometers measure the aerosol spectral optical thickness and solar radiance; thus, only daytime and clear-sky conditions are considered. An inversion algorithm is applied to retrieve a set of aerosol properties [Dubovik and King, 2000], including the particle size distribution of aerosols between 0.05 μm and 15 μm. The retrieval assumes a plane-parallel atmosphere, vertically homogeneous distributed aerosol, and surface reflectance approximated by bidirectional reflectance distribution function. Nonsphericity of aerosol particles can also be accounted for by the spheroid model in remote sensing of desert dust [Mishchenko et al., 1997]. The data in Figure 2 are averages over the time period of 1996–2006. The case numbers indicate the observation in different dust source regions shown in Figure 1. All plots in Figure 2 exhibit continuous curves of the aerosol size distribution. An important feature for the observed size distribution in Figure 2 is the bimodal shape, with two peaks mostly located at around 0.2 μm and 3 μm. LI ET AL.

DUST SIZE DISTRIBUTION FOR RADIATION

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Figure 1. The locations of 24 dusty sites for AERONET inversion retrieval data. Africa (numbers 1–9, in yellow color), Middle East (10–15, in red), Caribbean-America (16–22, in blue), and elsewhere in the world (23–24, in purple).

The number size distribution of aerosol is expressed as n(r) =

dN dr

(1)

where r is the radius of the spherical aerosol particle and N is the concentration of aerosol. The relation of volume-size distribution to the number size distribution is [Sayer et al., 2012] dV 4𝜋 4 dN = r dlog(r) 3 dr

(2)

For nonspherical particles, r becomes the volume-equivalent radius rv = (3V∕4𝜋)1∕3 [Mishchenko et al., 1997]. The size distribution of aerosol can be characterized by two parameters of effective radius reff and effective m m m variance veff , which are defined as reff = m3 and veff = m2 2 4 − 1, with the moment defined as mi = ∫ ri n(r)dr 2

3

[Chylek et al., 1992]. In Figure 1, reff and veff are listed for each case. The aerosol optical properties required for radiative transfer (without considering polarization) are the specific extinction, single-scattering albedo, and asymmetry factor. For a particle of radius r, specific extinction at wavelength 𝜆 is 𝜋Qext (r, 𝜆)r2 𝜓𝜆 (r) = (3) DAC where Qext (r, 𝜆) is the extinction efficiency and DAC is the dust aerosol content DAC = 4𝜋∕3𝜌a r3 [Kiehl et al., 2000], where 𝜌a is the aerosol mass density. The single-scattering albedo specifies the fraction of the total radiation interacting with a particle (through scattering and absorption processes) that is scattered. It is defined as 𝜔𝜆 (r) =

Qsca (r, 𝜆) Qext (r, 𝜆)

(4)

where Qsca is the scattering efficiency. The phase function, P, describes the angular distribution of scattered photons for scattering events. The phase function for particle of radius r is given by P(𝜃, 𝜆) =

𝜆2 [i (𝜃, r, 𝜆) 2𝜋 2 1

+ i2 (𝜃, r, 𝜆)]

Qsca (r, 𝜆)r2

(5)

where 𝜃 is the scattering angle and i1 and i2 are the squares of the vertical and horizontal scattering amplitudes. The asymmetry factor is g, which is the integrated phase function weighted by the cosine of the scattering angle. LI ET AL.


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Figure 2. Aerosol volume-size distribution, dV∕d log(r) at 24 dusty sites from AERONET inversion retrieval data. Africa (numbers 1–9), Middle East (10–15), Caribbean-America (16–22), and elsewhere in the world (23–24). The AERONET site number is shown at the upper right corner; reff and veff are the effective radius and effective variance.

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The observed dust aerosol size distribution is measured in discrete data with 22 bins. The aerosol optical property should be calculated for each bin, since the scattering result is sensitive to particle size. We denote the size distribution for each bin as ni (i = 1, 2, · · · , m), m is the total number of bins with ri being the central point of bin i and Δi being the bin width. The aerosol number concentration for bin i is ni Δi . The specific extinction for bin i is 𝜋Qext (ri , 𝜆)ri2 ni Δi 𝜓𝜆 (ri ) = (6) DAC where DAC = 4𝜋∕3𝜌a ni ri3 Δi . Similarly, we can define the single-scattering albedo and asymmetry factor for each bin. Finally, the result from the individual wavelength is accumulated to form the band mean result and can be fed into the radiative transfer calculation. There will be b × m radiative transfer calculations required, where b is the number of bands for a band model or the number of k of a correlated k model [Sun and Rikus, 1999; Li and Barker, 2005]. In the dust optical property calculation, the refractive index provided by Balkanki et al. [2007] is used. It is found that these new data produce a better agreement with satellite and AERONET results in evaluation of mineral aerosol radiative forcings [Balkanki et al., 2007]. In order to avoid applying radiative transfer to each bin, a mean value of aerosol optical property is calculated for the whole size spectrum. The specific extinction is 𝜓𝜆 =

𝜋

∑m i=1

Qext (ri , 𝜆)ri2 ni Δi

DAC

(7)

∑m where DAC = 4𝜋∕3𝜌a i=1 ni ri3 Δi . The similar formulae are applied for the other optical properties. Using this method, only a number of b radiative transfer calculations are required, and the computing time is 1∕m of the detailed bin calculation.

In (7) an assembly mean value of the specific extinction is used for all aerosol sizes rather than separate values for each bin, because we are only interested in the mean radiation result. In principle, the assembly mean method based on (7) can be applied to the radiative calculation in climate models. However, though the assembly mean method is faster than the bin method, the Mie calculation for Qext (ri , 𝜆) is still time consuming. Further simplification can be done through the parameterization to avoid the direct Mie calculation, in which the aerosol optical property is precalculated based on an assumed particle size distribution. Usually, the aerosol size distribution is assumed to closely resemble the lognormal distribution as n(r) =

) ( N (ln r − ln r0 )2 dN = √ 0 , exp − dr 2(ln 𝜎)2 2𝜋r ln 𝜎

(8)

In equation (8), N0 is the total number density, r0 is the geometric mean radius (for the mode), and 𝜎 is the m m m geometric standard deviation. reff = m3 = r0 exp(2.5(ln 𝜎)2 ) and veff = m2 2 4 − 1 exp((ln 𝜎)2 ) − 1 [Chylek et al., 2 3 1992]. Thus, r0 and 𝜎 are determined by reff and veff . The gamma size distribution is also commonly used to resemble the particle size distribution. n(r) =

𝛽 𝛼+1 𝛼 −𝛽r dN = N0 r e dr Γ(𝛼 + 1)

(9)

where Γ is the gamma function and 𝛼 and 𝛽 are constant coefficients with relationship to the effective radius m m m and variance as reff = m3 = (𝛼 + 3)∕𝛽 and veff = m2 2 4 − 1 = 1∕(𝛼 + 3) [Chylek et al., 1992]. 2

3

In Figure 3, the observed size distributions are shown again but in the form of number concentration, n(r). Both of the lognormal and gamma distributions for each case are shown as well, which are determined by reff ∑m and veff as listed in Figure 2 for each case, and the total number density N0 = i=1 ni Δi from the observed data. In Figure 3, the observed size distributions show the bimode structure; however, the second mode is several orders of magnitude lower than the first mode. The curves of the lognormal and gamma distributions are smooth without showing bimode structure. Generally, both of the lognormal and gamma distributions can approximately simulate observed results. However, in a few cases, the difference between the assumed and observed size distributions could be considerably large, for example, the case 22 from the Caribbean-America LI ET AL.


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Figure 3. The green lines are the same dust aerosol size distributions as Figure 1 but plot in number concentration n(r). At the bottom of each panel, the first, second, and third numbers are the skewness values for observed size distribution, lognormal size distribution, and gamma distribution.

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site. This case presents very small reff but very large veff . It is shown that both of the lognormal and gamma size distributions produce a much lower number of concentrations in the particle size range shown in Figure 3. The calculations show that the total number concentrations are very close between the assumed size distribution and observed distributions. However, in the lognormal and gamma distributions, about 70% of particles fall into the range below 0.05 μm, since both the lognormal and gamma distributions start from very small radius and have very long tails. Therefore, the assumed distributions show much lower number concentrations in the plot range from 0.05 μm to 25 μm. The simulation to the observed size distribution fails in the case 22. Although the values of reff and veff in Figure 3 are the same for the three curves in each case, and the values of total particle number, N0 , are generally very close, other parameters for distribution can be different, for example, the skewness. Skewness is a measure of the asymmetry of the probability distribution of a real-valued variable about its mean [Johnson et al., 1994]. ] [( m3 − 3m1 𝜎 2 − m21 r − m 1 )3 𝛾= (10) n(r)dr = ∫ 𝜎 𝜎3 where m1 , m3 are the moments as defined above and 𝜎 = m2 − m21 is the standard deviation. In Figure 3, three skewness values are listed in each panel for the observed data, lognormal and gamma size distributions. All the values are positive, which means the distributions are all right skewed with long right tails. The values of skewness for the lognormal size distribution are always much smaller than the observed results only with the exception of the case 22. The smaller skewness means the distribution is not right skewed enough, which results in more particles remaining in the small size region. For gamma size distributions, the skewness values are generally very close to the observed results. In a parameterization for the aerosol optical property, the effects of the size distribution on the optical properties are accounted for in terms of reff and veff from the lognormal size distribution or gamma size distribution. The specific extinction is calculated based on a number of predetermined reff and veff , 𝜓𝜆 =

𝜋 ∫ Qext (r, 𝜆)r2 n(r)dr

DAC

,

(11)

Qext is the extinction efficiency, and the aerosol content is calculated as DAC = 4𝜋∕3 ∫ 𝜌a n(r)r3 dr. The similar treatment is for the other optical properties. We chose 10 predetermined reff (from 0.1 to 3.5 μm) and 6 predetermined veff (from 0.3 to 3.5). All the precalculated results are organized in a look-up table. For any pair of reff and veff , the aerosol optical properties can be obtained by an interpolation based on the 10 × 6 points from the look-up table. The computing time of the parameterization is 2 orders of magnitude less than that of the assembly mean method.

3. Comparison Results 3.1. Results From Radiative Transfer Models A one-dimensional radiative transfer model is used to investigate the sensitivity of dust radiative forcing to aerosol size distribution and other parameters. The radiation model uses a correlated k distribution scheme for gaseous transmission [Li and Barker, 2005]. Dust radiative forcing is calculated with the prescribed standard atmospheric profiles for midlatitude summer following McClatchey et al. [1972]. Surface albedo is set to 0.2, which is close to the global mean land surface value. The dust loading is set to the global mean column value of 0.0468 g m−2 , which is in good agreement with the result of AEROCOM (Aerosol Comparisons between Observations and Models) estimated from 10 GCM simulations [Schulz et al., 2006]. The dust concentration decreases with height. We choose a vertical profile with an exponential decay of concentration [Peng et al., 2012]. The aerosol radiative forcing is defined as the difference in the net (downward minus upward) radiative flux at tropopause (200 hPa) from two simulations, one with and the other without the aerosol. Figure 4 shows the dust shortwave radiative forcing at 200 hPa with a solar zenith angle varying from 0 to 90∘ . The green lines are results from the benchmark calculations as the radiative transfer model is applied to each bin, and the total aerosol forcing is the summation of the results from all bins. The grey lines are the results by the assembly mean method based on equation (7). It was found that the assembly mean method can always produce very accurate results since it was based on the true size distribution. The relative errors are generally less than 1%. The case 22 is the worst one, with relative error LI ET AL.


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Figure 4. Dust aerosol shortwave radiative forcing at tropopause (200 hPa). The green and grey lines are the results from benchmark and assembly mean calculations, respectively. The blue and red lines are the results from dust optical property parameterization based on the lognormal size distribution and gamma size distribution, respectively.

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of about 20%. We therefore conclude that the assembly mean can handle the aerosol size distribution in climate models. The blue lines are the results from the optical property parameterization based on the assumed lognormal size distribution. The accuracy becomes very poor with errors over 25% in most cases. In Figure 3 the lognormal size distribution always shows considerable bias to the observed size distribution. The small skewness values mean more particle numbers are shifted to the small size range. The scattering efficiency is much higher for small particles, which causes much larger reflection and larger aerosol radiative forcing. The red lines are the results from the optical property parameterization based on the assumed gamma size distribution. The accuracy is dramatically improved compared to the blue lines with errors generally less than 5%. This is expected since the gamma size distributions are less bias to the observed size distributions as show in Figure 2. In Figure 3 most red lines are below the blue lines. However, this is not the reason for the smaller radiative forcing in the gamma size distribution, since the absolute value of n(r) is not important for the aerosol optical property parameterizations. From equations (3)–(5), all calculations of optical properties rely on ratios with n(r) appearing both in the numerator and denominator. The result is only dependent on the relative size distribution for the assumed size distribution. The calculations show that the size range between 0.1 μm and 2 μm plays a dominant role for the dust radiative forcing. An accurate simulation of size distribution in this range is important. Figure 4 indicates that to some extent the parameterization based on the assumed gamma size distribution can produce accurate aerosol radiative forcing in climate models. Besides the data for the annual mean dust size distribution, we also have studied the monthly mean results for dust size distribution from the same AERONET observation data. In Figure 5, the monthly mean data for dust size distribution are shown for the site 9 in the center of the Sahara desert. The results from March to July are shown, since the dusty storms there mostly happen in the spring and summer seasons [Luo et al., 2015]. The left column shows the results of the dust size distribution in the form of dV∕dlog(r). Compared to Figure 2, the curves of the monthly mean size distributions became less smooth and the peaks became higher compared to the results of annual mean. Also, the distributions became narrower with much smaller values of effective variance. The middle column shows the size distribution in the form of n(r); also, the results from the lognormal and gamma size distributions are presented. Similar to the results of Figure 3, the skewness values from gamma size distributions are much closer to the observed results, which makes that the configurations of the gamma size distribution match more with the observed curves. Figure 5 (right column) shows the dust radiative forcing at 200 hPa. All the methods of detailed bin calculation, assembly mean, and parameterization based on the lognormal and gamma size distributions are considered. Again, the assembly mean method can always produce very accurate results, and the parameterization based on the assumed gamma size distribution is always much better in simulation of aerosol radiative forcing compared to the parameterization based on the lognormal size distribution. We have also considered the other types of aerosol with hydroscopic growth, like sulfate aerosol [Li et al., 2001]. Similar to dust, the aerosol radiative forcing is smaller for an optical property parameterization based on the gamma size distribution compared to that based on the lognormal size distribution. In the old bulk aerosol scheme, the detailed size distribution was not resolved. A two-mode scheme was used, which contains a fine mode (reff = 0.39, veff = 0.597) and a coarse mode (reff = 1.9, veff = 0.61) [Hess et al., 1998]. The aerosol size distribution is fixed for the two modes. From Figures 2 and 5, the dust size distribution does show a bimode pattern, but the sizes of the two modes change from case to case. In addition, mass portions for the two modes cannot be properly determined by the climate models. We found that it is impossible to obtain the accurate aerosol radiative forcing by tuning the mass portions of the two modes. Though most dusts are nonspherical particles, in current climate models almost all of the parameterizations for dust optical property are based on Mie calculation. The nonspherical effect is very small for small particles [Raisanen et al., 2012; Wang et al., 2013; Colarco et al., 2014]. For example, Wang et al. [2013] found that the global annual means of shortwave dust instantaneous radiative forcing due to spherical and nonspherical dust aerosols at the top of the atmosphere (TOA) for clear sky are −1.16 W m−2 and −1.14 W m−2 , respectively. The purpose of this study is to analyze the impact of aerosol size on radiative transfer. The methodology LI ET AL.


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Figure 5. (left column) Same as Figure 2 but for monthly mean data (March to July) at site 9, (middle column) same as Figure 3 but for monthly mean data at site 9, and (right column) same as Figure 4 but for monthly mean data at site 9.

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Difference in clear-sky planetary albedo (%) Difference in solar upward flux at TOA(Wm-2) (Gamma size distribution - lognormal size distribution ) (CanAM4 - CERES observation) December to February

March - May

June to August

September to November

Figure 6. (left column) Differences in clear-sky planetary albedo between CanAM4 and CERES observations. (right column) Differeces in upward shortwave radiative flux at TOA between the two dust optical property parameterizations based on the assumed gamma and lognormal size distributions.

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presented in this study is also applicable for the nonspherical case, as the skewness for the lognormal and gamma size distributions should be analyzed and compared with the observed results. 3.2. Results From GCM Dust plays an important role in climate change [Huang et al., 2014]. In the following section, we test the radiative impact in a climate model due to the use of two aerosol size distribution schemes discussed above. The model used here is the fourth generation of the Atmospheric Global Climate Model of the Canadian Center for Climate Modelling and Analysis (CanAM4) [von Salzen et al., 2013], which employs a spectral resolution of T63, with 38 vertical levels from the surface up to 1 mb. The simulation is forced by CMIP5 sea surface temperatures and sea ice extent averaged over the period of 2003–2008. The method proposed by von Salzen [2006] was used to simulate the aerosol size distributions. The instantaneous radiative difference is used to analyze the climate impact by using different schemes discussed above. In order to diagnose instantaneous impact, the radiation calculation is performed twice at each model integration time step. The first calculation uses the dust aerosol optical property parameterization based on the lognormal size distribution. The second calculation uses the dust optical property parameterization based on the gamma size distribution. The difference in net radiative flux between the two calculations reflects the effects due to the use of different aerosol size distributions. In the model integrations, the model fields are only updated using the radiative result from the first calculation, and therefore, there is no climate feedback from the second calculation. Figure 6 shows the results. Figure 6 (left column) presents the differences in clear-sky planetary albedo between modeled results from the first experiment and satellite observations (Clouds and the EarthŠs Radiant Energy System (CERES) EBAF-TOA data set [Loeb et al., 2009]). Though the global dust burden in CanAM4 is within the range of AEROCOM [Peng et al., 2012], it is seen that the modeled planetary albedos are overestimated in most Asia continent, part of Sahara desert in the North Africa and Atacama desert in South America. The overestimations in Asia continent are large in all seasons except in spring. However, the overestimation is spread across South America in spring season. Figure 6 (right column) shows differences in clear-sky upward fluxes at TOA between two experiments. The negative sign implies that the use of gamma distribution reduces amount of reflected solar fluxes, and the decrease of solar reflection is to 1 W m−2 in the Sahara desert and Atacama Desert. It is seen that the negative areas in Figure 6 (right column) are roughly the same as positive areas in Figure 6 (left column), which means that the use of gamma size distribution can reduce model biases in aerosol radiative forcing. It is found that the bias problem cannot be completely solved by the current study. By replacing the lognormal size distribution to the gamma distribution in dust optical property parameterization, the differences in clear-sky planetary albedo in the Sahara desert and Atacama Desert are only about 1–2% which are smaller than the results shown in Figure 6 (left column). The other physical factors, like the surface albedo, can also affect the result of planetary albedo. This study has led to partly improving the simulation in aerosol radiative forcing.

4. Conclusions The following conclusions can be drawn for this study: 1. The benchmark calculation for aerosol radiative forcing should be based on results from each bin. So far, there has been no effort to compare the aerosol optical parameterization against the benchmark result based on the true aerosol size distribution. In all earlier aerosol parameterization studies, the comparison is referred to the approximation calculation against the Mie calculation, but both are based on the assumed lognormal distribution. 2. The proposed assembly mean method can produce accurate results. The aerosol size information is directly collected in the assembly mean method without considering reff and veff . Since the aerosol optical property is summarized for the whole size domain, the number of radiative transfer calculations is reduced. However, the detailed Mie calculation is still computationally time consuming. The assembly mean method can be used to produce the standard results for climate models when the computing time is not an issue. 3. For a same pair of reff and veff , the aerosol size distributions still can be very different for the assumed lognormal or gamma size distributions. The skewness is another important value to judge how close the assumed distribution is to the observed result. It is found that the skewness for the lognormal size distribution is always smaller than that of the observed result. The smaller skewness values mean that more particle numbers are shifted to the small size range. The scattering efficiency is much higher for small particles, which LI ET AL.


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causes much larger reflection and larger aerosol radiative forcing. At least in the dust case, the skewness values of the gamma distribution are always much closer to the observed results. 4. The parameterization allows us to obtain the optical property directly by the precalculated data table based on an assumed size distribution. The computing is about 2 orders of magnitude faster than the assembly mean method. The parameterization based on the gamma size distribution can produce much more accurate results in radiative forcing compared to that based on the lognormal size distribution. However, today the lognormal size distribution is assumed for aerosol particle, and the gamma size distribution is assumed for cloud droplet [Chylek et al., 1992; Hess et al., 1998; Dobbie et al., 1999; Li et al., 2008]. More detailed investigations regarding size distribution for other types of aerosol and cloud are needed. In the two-parameter schemes of lognormal and gamma size distributions, the skewness is not an independent variable. However, it is important to make sure that the skewness values in parameterization match with the observation results or the climate model output results. 5. The result of CanAM4 was consistent with that from the offline single-column model. In current climate models, the dust radiative forcing could be overestimated by using the dust optical property parameterization based on the lognormal size distributions. Today, most of climate models are able to simulate the full aerosol size distributions. Besides the bin method, the modal aerosol model [Liu et al., 2012] can also simulate the aerosol size distribution properly. Therefore, the corresponding aerosol optical property parameterization accounting for size distribution is required, and the parameterization is based on the model output of reff and veff . Our study indicates that the size distributions between the model output and the assumed size distribution in parameterization should be consistent and the skewness is an important quantity to judge such consistency. Acknowledgments The authors thank three anonymous reviewers and K. von Salzen and J. Cole for their constructive comments and Zhanqing Li for his editorial effort. The authors acknowledge the AERONET aerosol size distribution data from http://www.atmos-chem-phys.net/11/ 7781/2011/acp-11-7781-2011supplement.pdf.

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