Effect of Particle Shape on Dust Shortwave Direct Radiative Forcing Calculations Based on MODIS Observations for a Case Study

Received 30 October 2014; revised 6 February 2015; accepted 12 February 2015

Dust aerosols, which from a radiative point of view are one of the most important atmospheric aerosol species, can affect the Earth's radiation budget and climate both directly and indirectly (King et al., 1999; Haywood and Boucher, 2000; Sokolik et al., 2001; Kaufman et al., 2002). The aerosol direct effect refers to the scattering and absorption of radiation by dust aerosols, while the indirect effect relates to dust aerosols modifying cloud albedo, cloud lifetime and the precipitation rate by acting as cloud condensation nuclei (Albrecht, 1989; Sekiguchi et al., 2003; Yi et al., 2012). Consequently, substantial effort has been made to improve our understanding of the dust aerosol radiative forcing of the Earth's climate system, largely via the use of radiative transfer and global climate models (Liao and Seinfeld, 1998; Myhre and Stordal, 2001; Christopher and Jones, 2008). In these studies, it is fair to say that large uncertainty still exists in terms of the quantitative assessment of dust aerosol direct radiative forcing, which depends critically on the optical properties of dust, such as the aerosol optical depth, single scattering albedo, and asymmetry factor. The uncertainty in estimating direct radiative forcing is partially due to the inherent difficulties in accurately determining the geometric size, morphology and mineralogical composition of dust particles, as well as their associated single scattering properties (Sokolik et al., 2001; Reid et al., 2003). Moreover, the direct radiative forcing of dust aerosols also depends on external conditions such as the solar zenith angle, underlying surface reflectance, and mixing processes during their transport (Lin et al., 2013; Yi et al., 2014a).

Dust aerosols primarily originate from arid and semi-arid regions, and can be transported over a large distance from their source regions. A special issue posed by dust aerosols is their predominantly complex and nonspherical particle shapes, particularly for coarse-mode dust (Koren et al., 2001; Okada et al., 2001), which means that the Lorenz-Mie theory is not applicable for computing their single scattering properties. Modeling results, together with several laboratory experiments (West et al., 1997; Volten et al., 2001; Curtis et al., 2008), have revealed that the scattering properties of realistic dust aerosols differ significantly from those based on spherical particles. As dust particles do not have any preferential shape, it is impractical to specify the morphological details of realistic dust particles in single scattering computation. In addition, most existing scattering-computational methods, such as the Discrete Dipole Approximation (DDA) method (Draine and Flatau, 1994) and the Finite Difference Time Domain (FDTD) method (Yee, 1966), require substantial computational resources and are not practical for coarse-mode dust particles, although these methods are flexible in computing the single scattering properties of irregularly shaped particles. As a result, dust particles are still often specified as spheres in radiative transfer simulations and remote sensing applications. As a reasonable approximation, the overall shapes of dust aerosols can be specified as simple as spheroids (Dubovik et al., 2006; Yang et al., 2007), which only introduce one additional parameter compared to homogeneous spheres. For spheroidal dust particles, the T-matrix method (Mishchenko and Travis, 1994; Bi and Yang, 2014) and geometric optics method (Yang and Liou, 1996) are generally employed to compute their single scattering properties. The scientific justification for using spheroidal particles in reproducing the scattering properties for nonspherical dust aerosols has been extensively approved in previous studies (Mishchenko et al., 1997; Nousiainen and Vermeulen, 2003; Dubovik et al., 2006; Merikallio et al., 2011).

It is generally acknowledged that neglecting the nonsphericity of dust particles may lead to substantial errors in the remote sensing of dust aerosol optical depths by employing satellite radiance measurements (Mishchenko et al., 2003; Zhao et al., 2003). However, there are still some discrepancies as to the significance of the particle shape effect for applications such as direct radiative forcing estimations of dust aerosols, in which only radiative fluxes are adopted. (Mishchenko et al., 1995) argued that the shape of dust particles becomes less important and should not introduce significant errors in radiative forcing calculations based on the fact that spheroids and spheres have very similar single scattering albedo and asymmetry factors. (Fu et al., 2009), for example, reported that very minor radiative flux differences exist between spheroidal and spherical particles, and concluded that the scattering properties based on the spherical particle shape assumption were suitable for dust aerosol direct radiative forcing calculations. In contrast to the studies cited above, (Pilinis and Li, 1998) found that a poor description of particle shape may lead to substantial errors in estimates of dust aerosol direct radiative forcing. Furthermore, Kahnert et al. (2005, 2007) re-evaluated the effects of particle shape in flux simulations and concluded that the use of spherical particles can introduce substantial errors in simulated dust aerosol radiative forcing. More recently, (Yi et al., 2011) concluded that the effect of particle shape can lead to a 30% difference in the dust direct radiative forcing at the top of the atmosphere (TOA) by employing triaxial ellipsoids to represent realistic dust aerosols. Using a global aerosol-climate model, (Haapanala et al., 2012) and (Colarco et al., 2014) studied the impact of particle shape on the shortwave direct radiative effect of dust by comparing simulation results based on spheroidal and spherical particle shape assumptions and found that the influence of particle shape on the modeled radiative effect of dust can be neglected. It is important to emphasize that the conclusions from the above-mentioned studies are, to the best of our knowledge, mostly based on the hypothesis that dust aerosol optical depth is prescribed beforehand. However, in some cases, when dust aerosol optical depths employed for radiative forcing estimation are derived directly from a remote sensing technique, it is more meaningful to take into account the effect of particle shape on the retrieved dust optical depths and hence on their direct radiative forcing estimations.

Assuming spheroidal and spherical particle shapes for dust aerosols, the present sensitivity study is intended to further improve current understanding of the effect of particle shape on dust direct radiative forcing calculations. To this end, we follow the method introduced by (Zhang et al., 2009), and study the effect of particle shape on dust direct radiative forcing in the following two aspects. First, the effect of particle shape on the single scattering properties of dust aerosols and the associated dust direct radiative forcing is assessed, without considering the effect induced by particle shape on dust aerosol optical depth retrievals. Second, the effect of particle shape on dust direct radiative forcing is further discussed by including the effect of particle shape on the retrieved dust aerosol optical depths. Regarding this latter aspect, the measurements from the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument, designed specifically to observe the spatial and temporal distributions of aerosols on the global scale, are used for a case study to address the effect of particle shape on dust aerosol optical depth retrievals and hence on dust direct radiative forcing calculations. For brevity, we exclusively focus on the instantaneous shortwave direct radiative forcing (SWDRF) of dust at the TOA in this study. The remainder of the paper is organized as follows. Section 2 describes the scattering computational method and radiative transfer model employed in this study. The algorithm for dust aerosol optical depth retrievals is also presented in this section. The major results of the study are discussed in section 3, and conclusions are summarized in section 4.

The dust aerosol optical depth retrievals and radiative forcing simulations for the current sensitivity study require the bulk scattering properties of dust aerosols. While realistic dust aerosol particles usually exhibit a myriad of complex morphologies, here we assume the particle shapes of dust aerosols to be spheroids or spheres. For the spheroidal particle shape assumption, dust particles are assumed to be a mixture of randomly oriented spheroids of various particle sizes and shapes, and the corresponding bulk scattering properties are derived by integrating the single scattering properties of individual particles over size and shape distributions. Since there is no single scattering computational code that can cover the size parameters ranging from the Rayleigh to geometric optics regimes, we use the T-matrix method (Mishchenko and Travis, 1994) to calculate the scattering properties for particles with small and moderate size parameters (less than 50) and an approximate method based on the improved geometric optics method (IGOM) (Yang and Liou, 1996; Yang et al., 2007) for particles with large size parameters (larger than 50). Note that the aforementioned IGOM takes into account the edge effect for the extinction efficiency and the above-/below-edge effects for the absorption efficiency (Yang et al., 2007). The technical details concerning the combination of the two scattering computational methods are illustrated with more discussion in (Dubovik et al., 2006) and (Yang et al., 2007). To describe the shape distribution of spheroidal dust particles, we consider an ensemble of spheroids with 20 aspect ratios distributed logarithmically equidistant between 0.3 and 3.3. Here, the aspect ratio of a spheroidal particle is defined as the ratio of the rotational-axis length (m) to the equatorial-axis length (n) of the particle. Note that m/n>1 and m/n<1 represent prolate and oblate spheroids, respectively. For simplicity in the present sensitivity study, the dust particle size distribution is treated as a single mode log-normal function in terms of particle number concentration, which is given by

\begin{equation} \label{eq1} \dfrac{dn(r)}{d\ln r}=\dfrac{N_0}{\sqrt{2\pi}\ln\sigma_g}\exp\left[-\dfrac{(\ln r-\ln r_g)^2}{2(\ln\sigma_g)^2}\right] , \end{equation}

where r is the radius of a spherical particle that has the same volume as a spheroidal particle, N₀ is the number concentration, and r_g and σ_g are the median radius and standard deviation of the monomodal distribution, respectively. Altogether, 1000 size bins ranging from 0.02 to 20.0 μm are considered for the particle size distribution. It is well known that the size distribution parameters that determine dust particle effective sizes are highly uncertain and vary from region to region, relying on such factors as geographic location and the age of dust aerosols. In addition, the variation in these parameters leads to uncertainties in the simulation of the scattering properties of dust aerosols. Here, consistent with prior measurements of feldspar dust particle size (Volten et al., 2001), we assume that the effective radius and effective variance for dust aerosols are 1.0 μm and 1.0, respectively. Thus, for a monochromatic wavelength of interest, the bulk scattering properties of spheroidal dust particles can be calculated, in the case of single scattering albedo, as follows:

\begin{equation} \overline{\omega(\lambda)}=\dfrac{\sum_{k=1}^{20}w_k\int_{r_{\min}}^{r_{\max}}Q_{\rm s}(\varepsilon_k,r,\lambda)A(r)\frac{dn(r)}{d\ln r}d\ln r} {\sum_{k=1}^{20}w_k\int_{r_{\min}}^{r_{\max}}Q_{\rm e}(\varepsilon_k,r,\lambda)A(r)\frac{dn(r)}{d\ln r}d\ln r} , \end{equation}

where Q _s and Q _e are the scattering and extinction efficiencies, respectively; ε_k is the aspect ratio of a spheroidal particle; Λ is the wavelength; A(r) is the corresponding projected area; and w_k denotes the weight of spheroidal particles with aspect ratio ε_k. The projected area (A) of a spheroid particle is one quarter of its surface area (S), and the surface area of a spheroid can be formulated as follows:

\begin{equation} \label{eq2} S=\left\{ \begin{array}{l@{\quad}l} 2\pi n^2+\pi\dfrac{m^2}{\varepsilon}\ln\dfrac{1+\varepsilon}{1-\varepsilon} & ({\rm oblate})\\[4mm] 2\pi n^2+2\pi\dfrac{mn}{\varepsilon}\sin^{-1}\varepsilon & ({\rm prolate}) \end{array} \right. , \end{equation}

where ε is the eccentricity of the spheroid.

The weights for different aspect ratios used in this paper are the same as those in our previous research, which are derived using the Monte Carlo method to obtain the best fit of the theoretically simulated phase matrix to the measured results for feldspar dust samples at a wavelength of 0.441 μm (Feng et al., 2009). Specifically, particles with aspect ratios that deviate considerably from unity carry more weight than quasi-spherical particles. It is important to note that the shape distribution of spheroids used in the present sensitivity study may not represent the actual shapes of dust aerosols, although they can reproduce the scattering phase matrix better than spheres (Dubovik et al., 2006). As for spherical dust particles, the Lorenz-Mie theory is employed to compute the single scattering properties, and the corresponding bulk scattering properties are similarly derived by integrating the single scattering properties of individual spherical dust particles over the particle size distribution. The size distribution used here for spherical particles is the same as in the case with spheroidal particles. Note that Eq. (2) can also be used to calculate the bulk scattering properties of spherical dust aerosols if the weight is replaced by unity.

To investigate and quantify the effect of particle shape on the retrieved dust aerosol optical depths, the aerosol retrieval algorithm used in the present sensitivity study follows the Deep Blue aerosol retrieval algorithm, as illustrated in detail by Hsu et al. (2004, 2006), which was originally developed to retrieve dust aerosol optical depths over bright reflecting surfaces. Three MODIS channels (0.412, 0.47, and 0.65 μm) are employed in the Deep Blue algorithm based on the commonly used lookup table technique.

Similar to other aerosol retrieval algorithms, the present algorithm is based on the best match between the measurements and precalculated lookup tables. The lookup tables are developed with respect to the satellite-sun geometry (i.e., the satellite/sun zenith angle and relative azimuthal angle), underlying surface reflectance, dust optical depth, and single scattering albedo. Specifically, a total of 1728 angular combinations with 9 solar zenith angles (6^°, 12^°, 24^°, 36^°, 48^°, 54^°, 60^°, 66^° and 72^°), 12 satellite view zenith angles (0^° to 66^° in increments of 6^°), and 16 relative azimuthal angles (0^° to 180^° in increments of 12^°) are used to calculate the TOA radiances in the lookup tables. Five values of dust optical depth (0.0, 0.5, 1.0, 1.5, 2.0), which are referenced to 0.47 μm, are considered, ranging from a pure Rayleigh atmosphere to a highly turbid atmosphere. The MODIS level 1B products, which provide well calibrated and geolocated radiances with 1 km resolution, are employed to retrieve the dust optical depths. To study the effect of particle shape on the retrieved dust aerosol optical depths, lookup tables are developed for the spheroidal and spherical particle shape assumptions, respectively. Since prior knowledge of surface reflectance is needed for implementing aerosol retrievals, the surface reflectance is assumed to be Lambertian for simplicity and the Lambert-equivalent reflectance for each channel used in aerosol retrievals is estimated approximately based on the minimum reflectivity technique (Herman and Celarier, 1997; Koelemeijer et al., 2003).

Neglecting polarization may cause errors in the simulated TOA radiances for a Rayleigh-scattering atmosphere, especially for short wavelengths. For example, the differences of the simulated TOA radiances at the MODIS 0.47 μm channel between a polarized and unpolarized radiative transfer model may lead to a significant error for dust optical depth retrievals (Levy et al., 2004). The importance of considering polarization in the remote sensing application has also been proven by (Yi et al., 2014b). For this reason, a polarized radiative transfer code developed by De Haan et al. (1987), based on the adding-doubling method, is used to establish the lookup tables for aerosol retrievals, although the MODIS instrument does not measure polarized radiances. In this radiative transfer code, the Stokes vectors, denoted as I,Q,U, and V, are included and a radiation beam can be completely characterized by its intensity and state of polarization. Real atmosphere is usually vertically inhomogeneous, but here, for simplicity, the atmosphere is assumed to consist of a number of uniform and homogeneous layers, each of which is specified in terms of single scattering albedo, dust optical depth and scattering matrix. The atmospheric Rayleigh optical depth is calculated approximately as a function of wavelength (Dutton et al., 1994). The vertical distribution of dust aerosol layers in the atmosphere is set by a Gaussian function with a peak optical depth at 3 km over the underlying surface. Note that the scattering matrix for randomly oriented spheroidal particles has a block-diagonal form with six independent nonzero elements, given by

\begin{equation} P(\Theta)=\left[ \begin{array}{c@{\quad}c@{\quad}c@{\quad}c} P_{11}(\Theta) & P_{12}(\Theta) & 0 & 0 \\[1.5mm] P_{12}(\Theta) & P_{22}(\Theta) & 0 & 0 \\[1.5mm] 0 & 0 & P_{33}(\Theta) & P_{34}(\Theta) \\[1.5mm] 0 & 0 & -P_{34}(\Theta) & P_{44}(\Theta) \end{array} \right] , \end{equation} where Θ is the scattering angle. For spherical particles, the scattering matrix has only four independent elements, since P₁₁(Θ)=P₂₂(Θ) and P₃₃(Θ)=P₄₄(Θ).

For radiative forcing calculations, the radiative transfer model originally developed by (Fu and Liou, 1993) is employed to calculate the hemispherical flux at the TOA for both dust and pristine conditions. The model is a delta-four stream radiative transfer code with six solar spectral bands from 0.175 to 4.0 μm for the shortwave flux calculations and twelve infrared spectral bands between 2850 and 0 cm^-1 for the longwave flux calculations. The model has the ability to account for molecular Rayleigh scattering, various gas absorption, as well as absorption and scattering due to aerosols and clouds. The atmosphere is divided into 34 layers, and inside each layer dust optical properties are prescribed to be uniform and homogeneous. Vertical profiles of temperature, pressure, ozone, and water vapor mixing ratios are from the standard midlatitude atmosphere (COESA, 1976) and the underlying surface reflectance is assumed to be constant for the complete range of solar spectral bands in this sensitivity study. More specifically, the solar-weighted band averaged scattering properties for each solar spectral band are needed as inputs to this radiative model, which are calculated in the case of band averaged single scattering albedo as follows:

\begin{equation} \label{eq3} \overline{\overline{\omega}}=\dfrac{\int_{\lambda_1}^{\lambda_2}S(\lambda)\overline{\omega(\lambda)}d\lambda} {\int_{\lambda_1}^{\lambda_2}S(\lambda)d\lambda} , \end{equation}

where S(Λ) is the solar spectrum at the TOA, \(\overline\omega(\lambda)\) is the spectral single scattering albedo, and \(\overline\overline\omega\) is the solar-weighted value for the band between Λ₁ and Λ₂. Note that the spectral single scattering albedo used in Eq. (4) refers to the bulk scattering properties of dust particles, which can be computed using Eq. (2). The solar-weighted band averaged asymmetry factor and extinction efficiency can be obtained in the same way. For simplicity in this sensitivity study, we only run this model to calculate the instantaneous SWDRF of dust at the TOA. The SWDRF of dust at the TOA can be simplified as the difference between clear and dusty sky diffuse upward fluxes:

\begin{equation} \label{eq4} {\rm SWDRF}=F_{\rm c,TOA}\uparrow-F_{\rm d,TOA}\uparrow , \end{equation}

where F _c,TOA↑ and F _d,TOA↑ are the upward SW fluxes at the TOA for clear and dusty sky conditions, respectively. Positive (negative) SWDRF at the TOA indicates dust aerosols produce a warming (cooling) effect for the whole surface-atmosphere system.

Figure 1.  Comparisons of the simulated phase matrix between spheroidal and spherical dust particles for the MODIS 0.47 μm channel.

Based on the scattering computation methods as introduced in section 2, Fig. 1 shows the simulated dust aerosol phase matrix based on the spheroidal particle shape assumption for the MODIS 0.47 μm channel. For comparison, the corresponding results based on spherical particles are also shown in this figure. The effective radius and effective variance, which characterize the particle size for dust aerosols, are assumed to be 1.0 μm and 1.0, respectively. The complex refractive index of dust aerosols is assumed to be 1.55+0.003i in this simulation. As generally acknowledged, the simulated phase function P₁₁ based on the spheroidal particle shape assumption agrees quite well with the corresponding results related to spherical particles in the forward scattering directions. However, the spherical counterpart deviates substantially from the spheroidal results in side-scattering and back-scattering directions. The phase matrix element of P₂₂/P₁₁, known as a sensitive indicator for particle nonsphericity, is always 1.0 for spherical particles, whereas its counterpart for spheroidal particles varies significantly as a function of scattering angle. The degree of linear polarization, -P₁₂/P₁₁, which is important for the polarimetric remote sensing of aerosols, is also quite different between spherical and spheroidal particles. As for other elements of the phase matrix (e.g., P₃₃/P₁₁, P₃₄/P₁₁ and P₄₄/P₁₁), substantial differences are also observed in the case of spheroidal particles, as compared with the case of spherical particles.

In the Fu-Liou radiative transfer model, the bulk scattering properties of dust aerosols over each solar spectral band act as the inputs for radiative forcing calculations. Figure 2 presents comparisons of the bulk scattering properties between spheroidal and spherical dust particles in the solar spectral region ranging from 0.25 μm to 4.0 μm. The corresponding refractive index database for dust aerosols is taken from (D'Almeida et al., 1991). As evident from Fig. 2, spectral variation of bulk scattering properties of dust aerosols can be noted for both spheroids and spheres as a general feature. Specifically, the minimum value of single scattering albedo is found at the shortest wavelength, which indicates the strongest absorption. The value of asymmetry factor is the largest at the shortest wavelength and decreases with increasing spectral wavelength. Figure 2 also shows that the differences of the bulk scattering properties between spheroidal and spherical particles are less obvious, but do exhibit small differences. However, excellent agreement between these two particle shape assumptions is noticeable for single scattering albedo. This agrees well with (Mishchenko et al., 1995), who suggested that single scattering albedo is practically less sensitive to particle shape than other single scattering properties. Spheres and spheroids also produce very similar values for extinction efficiency and asymmetry factor, and the corresponding relative differences due to the use of spherical particles to represent spheroidal particles are quite small. In addition, it is also evident that the asymmetry factors for spheroidal particles are always slightly larger than those for spherical particles, which means that the spheroidal particles scatter more energy in the forward hemisphere when compared with their counterparts for spherical particles.

In order to investigate and quantify the effect of particle shape on dust shortwave direct radiative forcing calculations, we first evaluate the effect of particle shape on remote sensing retrievals of dust optical depths based on the MODIS observations. The lookup tables related to spheroids and spheres are separately employed for dust optical depth retrievals with a simplified aerosol retrieval algorithm, which is based on the aforementioned Deep Blue aerosol retrieval method. Figure 3 shows an example of a dust storm across the Gobi desert by using a MODIS Level-1b visible granule over Northern Asia on 27 May 2008. The area indicated by the red box is focused for the retrieval of dust aerosol optical depths in the present sensitivity study, and high dust-loading is prevalent throughout most of the area. Since cloud contaminated pixels cannot be selected for the remote sensing of aerosols, the normalized difference dust index (Qu et al., 2006), a dust detection method using MODIS 2.13 and 0.47 μm measurements, is employed here to distinguish mineral dust from clouds.

Figure 2.  Comparisons of the bulk scattering properties (extinction efficiency, single scattering albedo and asymmetry factor) between spherical and spheroidal dust particles in the spectral region ranging from 0.25 to 4.0 μm.

The lookup tables for the simulated TOA reflectance as a function of aerosol optical depth and single scattering albedo for 0.412 versus 0.650 μm (top panel) and 0.470 versus 0.650 μm (lower panel) are depicted in Fig. 4. The dotted and solid lines indicate the results based on the spheroid and sphere particle shape assumptions, respectively. The surface reflectances for different wavelengths are also shown in this figure. The scattering angle, which is related to satellite-sun geometry, is 145^°. As evident from this figure, the retrieved dust optical depths for this scattering angle can be underestimated if dust particles are assumed to be spheres in aerosol retrievals. The impact of particle shape on remote sensing retrievals of dust optical depths is considered in Fig. 5, which displays comparisons of the retrieved dust optical depths between the spheroidal and spherical particle shape assumptions. The corresponding scattering angle contours are also shown with black lines in this figure. As shown in this figure, the overall patterns of these two retrieved results are qualitatively similar; however, it is still noticeable that the retrieved values based on the spheroidal particle shape assumption are rather different from their counterparts based on the spherical particle shape assumption. The averaged dust optical depth for this case study is ∼20% larger for spheroids than for spheres. A more detailed comparison between these two retrieved results is clearly illustrated by Fig. 6. It is obvious that the retrieved dust aerosol optical depths for spheroids can be either larger or smaller than those for spheres, depending strongly on the scattering angles at which dust aerosol optical depths are retrieved. For example, at medium dust-loading conditions, the dust aerosol optical depths retrieved from the spherical particle shape assumption are slightly larger (typically by 10%) than their spheroidal counterparts for scattering angles ranging from 125^° to 129^°. For scattering angles larger than 143^°, the retrieved dust optical depths for spheroids are always larger than those for spheres, in particular for scattering angles ranging from 152^° to 156^°, for which the retrieved dust optical depths can be 40% larger for spheroids than for spheres. In addition, the differences between the retrieved dust optical depths based on the spheroidal and spherical particle shape assumptions become larger and larger as the scattering angle increases. These characteristics can be well illustrated by the comparisons of phase function between spheroidal and spherical particles, as shown in Fig. 1. As indicated, the phase function from the spheroidal particle shape assumption is larger than its spherical counterpart for scattering angles between 125^° and 129^°. According to the assumption of single scattering approximation, the retrieved dust aerosol optical depth is inversely proportional to the phase function, and therefore the retrieved dust aerosol optical depths for spheroidal particles are smaller than their spherical counterparts. Furthermore, the differences of retrieved dust aerosol optical depths due to the use of spherical particles to represent spheroidal particles can be comparable to the actual values of retrieved dust aerosol optical depths for some scattering angles. These results shown in Fig. 5 and Fig. 6 clearly demonstrate that the effect of particle shape cannot be neglected for remote sensing retrievals of dust aerosol optical depths.

Figure 3.  MODIS Level-1b visible granule showing a dust plume over North Asia on 27 May 2008. The area indicated by the small red box is used to retrieve dust aerosol optical depth in the present sensitivity study.

Figure 4.  The simulated TOA reflectance as a function of aerosol optical depth and single scattering albedo for 0.412 versus 0.650 μm (top panel), and 0.470 versus 0.650 μm (lower panel). The dotted and solid lines indicate the results based on the spheroidal and spherical particle shape assumptions, respectively.

Figure 5.  Comparisons of the retrieved dust optical depths between the spheroidal and spherical particle shape assumptions. The results for the spheroidal and spherical particle shape assumption are shown in the left-and right-hand panel, respectively.

Figure 6.  Differences of the retrieved dust aerosol optical depths between the spheroidal and spherical particle shape assumptions.

Figure 7.  Comparisons of the SWDRF at the TOA between spheroidal and spherical dust particles for different surface\quad reflectances.

Without considering the effect of particle shape on the retrieved dust aerosol optical depths, comparisons of the instantaneous SWDRF of dust at the TOA between spheroidal and spherical particle shape assumptions, as a function of dust aerosol optical depth in units of W m^-2 for different solar zenith angles, are shown in Fig. 7. That is, the dust optical depths are prescribed a priori in radiative forcing calculations. The bulk scattering properties as shown in Fig. 2 are integrated using Eq. (5) to obtain the solar-weighted band averaged scattering properties, which act as inputs for radiative forcing calculations. An averaged broadband surface reflectance of 0.05 is employed for simplicity, although the surface reflectance varies as a function of wavelength (Haapanala et al., 2012). Two values of solar zenith angle corresponding to different local times are considered here for the spheroidal and spherical particle shape assumptions. As can be seen from Fig. 7, the SWDRF of dust at the TOA is quite sensitive to the solar zenith angle and dust aerosol optical depth. For the cases we have studied, the increase of dust optical depth (solar zenith angle) strengthens the negative radiative forcing (cooling) at the TOA. Moreover, compared with spheres, spheroids have a larger asymmetry factor, which acts to reduce the negative SWDRF at the TOA for fixed dust aerosol optical depth and solar zenith angle. Also evident from this figure, the use of spherical particles to represent spheroidal particles can only lead to a minor overestimation of at most 5% for radiative forcing calculations. It is important to note that the minor differences in the SWDRF at the TOA between spheroids and spheres stem directly from the differences of the bulk scattering properties between the different particle shape assumptions. These results seem consistent with (Mishchenko et al., 1995) and (Fu et al., 2009), in that the effect of particle shape on the dust direct radiative forcing can be negligible and the Lorenz-Mie theory can be used for computation provided the dust aerosol optical depths are already known.

Figure 8.  Comparisons of the simulated SWDRF of dust at the TOA between the spheroidal and spherical particle shape assumptions as a function of dust aerosol optical depth for different solar zenith angles.

Figure 9.  Left panel: scatter plots of the SWDRF at the TOA for spherical dust versus spheroidal dust. Right panel: the corresponding relative differences for the SWDRF of dust at the TOA between the spheroidal and spherical particle shape assumptions.

With remote sensing retrieved dust optical depths employed for radiative forcing calculations and the effect of particle shape on retrievals taken into account, comparisons of the instantaneous SWDRF at the TOA between spheroidal and spherical particle shape assumptions are shown in Fig. 8. The rows and columns correspond to different surface reflectances (A_S=0.05 or 0.15) and particle shapes (spheroids or spheres), respectively. As indicated by this figure, the spatial distributions of the SWDRF and the associated dust optical depths (as shown in Fig. 5) are consistent, and regions with high dust optical depths unsurprisingly correspond to high-magnitude SWDRF. As expected, due to the differences of the retrieved dust optical depths between spheroids and spheres, the corresponding differences of the SWDRF at the TOA are also obvious, and spheroids generally produce stronger negative forcing than spheres. For example, for the case of A_S=0.05, the averaged SWDRF at the TOA is about -45.9 W m^-2 for spheroids and -37.2 W m^-2 for spheres. As A_S is equal to 0.15, the corresponding values of SWDRF for spheroids and for spheres are -16.2 W m^-2 and -12.1 W m^-2, respectively. Furthermore, it is important to note that increasing A_S reduces the differences of the SWDRF between spheroids and spheres.

A scatterplot of the simulated SWDRF of dust at the TOA between spheroidal and spherical particles is color-coded according to different scattering angles, as shown in the left panel of Fig. 9. It is important to emphasize that the effect of particle shape on dust aerosol optical depth retrievals is taken into account in radiative forcing calculations. Magnitude differences in the SWDRF at the TOA between spheroidal and spherical particles are highly related to the differences in the retrieved dust aerosol optical depths. For scattering angles ranging from 125^° to 129^°, the spheroidal particle shape assumption leads to smaller dust optical depths and decreased negative SWDRF at the TOA. Meanwhile, spheroids have a larger asymmetry factor, which also leads to decreased negative SWDRF. For scattering angles larger than 143^°, the opposite is observed and the spheroidal particle shape assumption leads to larger dust optical depth and increased negative SWDRF at the TOA, although the larger asymmetry factor and optical depths of spheroids partly cancel each other's radiative effects.

The right-hand panel of Fig. 9 shows the relative difference ε_F of the SWDRF of dust at the TOA on the basis of these two particle shape assumptions as a function of dust aerosol optical depth for different scattering angles. The ε_F is defined as

\begin{equation} \label{eq5} \varepsilon_F=\left|\dfrac{\Delta F_{\rm sphere}-\Delta F_{\rm spheroid}}{\Delta F_{\rm spheroid}}\right| , \end{equation}

where ∆ F _sphere and ∆ F _spheroid represent the SWDRF of dust at the TOA based on the spherical and spheroidal particle shape assumptions, respectively. As evident from this figure, the values of ε_F depend critically on the scattering angles at which the dust aerosol optical depths are retrieved. For scattering angles ranging from 125^° to 129^°, the averaged ε_F is about 10%, which is close to the 40% for scattering angels ranging from 152^° to 156^°. Moreover, the values of ε_F at low dust-loading conditions can exceed up to 40%, as indicated for scattering angles within the range from 152^° to 156^°. And the effect of particle shape becomes less important at high dust-loading conditions where multiple scattering processes dominate. The results shown in Fig. 9 clearly demonstrate the effect of particle shape on the dust radiative forcing calculations for an instantaneous case study cannot be neglected provided the effect of particle shape on the retrieved dust aerosol optical depths are taken into account for radiative forcing calculations.

Taking advantage of existing sophisticated scattering computation methods and radiative transfer models, the present reported work examines the impact of particle shape on dust shortwave direct radiative forcing calculations based on the MODIS observations for a case study. To this end, we first study the effect of particle shape on remote sensing retrievals of dust optical depths, which are generally employed to estimate the dust direct radiative forcing. Two major particle shapes, spheroid and sphere, are considered here, and the single scattering properties of spheroidal dust particles are simulated based on a combination of the T-matrix method and the IGOM, whereas the Lorenz-Mie theory is employed for spherical particles. Lookup tables related to spheroids and spheres are separately constructed for dust optical depth retrievals with a simplified aerosol retrieval algorithm, which is based on the Deep Blue aerosol retrieval method.

The results reveal that the effect of particle shape on the retrieved dust aerosol optical depths cannot be neglected due to the pronounced differences of phase function between spheroids and spheres, especially in terms of side-scattering and back-scattering directions. And the retrieved dust optical depths based on spheroidal particles can be either larger or smaller than those based on spherical particles, depending critically on the scattering angles at which dust optical depths are retrieved. For example, the relative differences of retrieved dust optical depths between spheroids and spheres can be as large as 40% for medium dust-loading conditions. As for the effect of particle shape on dust direct radiative forcing calculations, we use the Fu-Liou radiative transfer model (Fu and Liou, 1993) to simulate the SWDRF of dust at the TOA for cloud-free conditions. The following two aspects are considered in the sensitivity study. First, the effect of particle shape on the single scattering properties of dust aerosols and associated dust direct radiative forcing is evaluated, without considering the effect induced by particle shape on dust aerosol optical depth retrievals. The results indicate that the differences of scattering properties (e.g., single scattering albedo, extinction efficiency and asymmetry factor) between spheroidal and spherical dust aerosols are negligible, which can lead to a relative difference of at most 5% for radiative forcing calculations. Second, the effect of particle shape on dust direct radiative forcing is further discussed by involving the effect of particle shape on the retrieved dust aerosol optical depths and hence on radiative forcing calculations. It is shown that the relative differences of radiative forcing between spheroids and spheres for an instantaneous case study can exceed up to 40% at low dust-loading conditions, depending critically on the scattering angles at which the dust aerosol optical depths are retrieved. Therefore, the effect of particle shape on dust instantaneous shortwave direct radiative forcing cannot be neglected provided the retrieved dust aerosol optical depths are employed for radiative forcing calculations. Furthermore, it should be emphasized that our results pertain specifically to the effect of particle shape on the instantaneous SWDRF; in the future, we intend to explore the particle shape effects on the diurnal mean SWDRF, which is more useful in climate studies.