The optical properties of aerosol particles are the basis for modeling their direct radiative forcing (Lacis and Mishchenko, 1995; Haywood and Boucher, 2000; Yi et al., 2011) and correspondingly for their effect on climate (McCormick and Ludwig, 1967; Myhre et al., 2013). Moreover, the optical properties are necessary for all inversion techniques used for aerosol remote sensing (Koepke and Quenzel, 1979; Kaufmann, 1993; Kalashnikova and Sokolik, 2002; Nousiainen, 2009). Thus, for an easy availability of spectral optical properties of aerosol particles, the software package OPAC (Optical Properties of Aerosols and Clouds) had been created (Hess et al., 1998).

The optical properties of aerosol particles in general are modeled using the size distribution and the spectral refractive indices of the particles. In the past, the assumption has commonly been made that the particles are spheres using Mie theory (Mie, 1908). This has different reasons: on the one hand, the assumption of spherical particles is reasonable in many cases, especially for water-soluble aerosol types under typical meteorological conditions with relative humidity higher than 50 %. On the other hand, the shape of individual particles is known only for a limited number of examples because it needs electron microscopy measurements. Thus, for actual conditions and for practical use, the shape of particles, particularly as function of size, is not available. But even if the particle shape were available, the problem remains that modeling of non-spherical particles would be complex and time consuming (Mishchenko et al., 2000; Kahnert, 2003). Thus, the use of Mie theory is often a good assumption (or the only possible assumption) and it has also been used in OPAC.

Desert aerosol, besides sea salt, forms the largest fraction of the atmospheric particles (d'Almeida et al., 1991; Kinne et al., 2006). Thus, desert aerosol is very important for the radiation budget and consequently for the climate, especially because it is distributed, often with high optical depth, over large areas. Since its amount shows very strong spatial and temporal variations (Sokolik et al., 2001), remote-sensing methods are important for desert aerosol research. However, remote-sensing is always based on the assumed particle characteristics.

Especially for mineral particles the optical properties modeled under the assumption of spherical shapes are questionable, since these particles are generated by mechanical processes which give rise to highly irregular particle shapes, as to be seen by electron micrographs (Falkovich et al., 2001; Kandler et al., 2011).

In comparison to spherical particles, the phase function of irregular particles generally shows increased sideward but reduced backward scattering if the particles are relatively large in comparison to the wavelength (Zerull et al., 1980; Koepke and Hess, 1988; Nousiainen, 2009; and see Fig. 1). Thus, if radiation data measured at short wavelengths are used to derive aerosol properties, the assumption of spheres may lead to wrong results. This holds also for particle properties derived from backscatter-lidar measurements (Gobbi et al., 2002; Wiegner et al., 2009; Sakai et al., 2014), since, amongst others, they are influenced by the lidar ratio, which combines backward scattering with the extinction coefficient. For passive remote-sensing from a satellite, an assumed wrong phase function of the particles can introduce significant retrieval errors and for consideration of the radiation budget of mineral particles in the solar spectral range, the assumption of spheres is a major source of error (Nousiainen, 2009). The amount of solar radiation scattered back to a radiometer at a satellite depends on the scattering angle, i.e. the angles of Sun and satellite, on the aerosol optical thickness, and on the reflectance at the ground. Thus the error in the case of assuming spherical particles is highly variable, and it is essential to use the appropriate scattering function (Horvath et al., 2006). The particle shape effect can cause up to 30 % difference in dust forcing at the top of the atmosphere (Yi et al., 2011).

These aspects are the reason for accounting for the non-sphericity of mineral particles in OPAC (Hess et al., 1998) and therefore improving this algorithm. The user-friendly database and software package OPAC presents the single-scattering properties of 10 aerosol components that are given with size distribution and spectral refractive indices for a spectral range from ultraviolet to far-infrared. These components can be easily combined by the user to individual mixtures, i.e. to variable aerosol types, for which phase functions and other optical and microphysical parameters are modeled after user request.

If a particle is no longer assumed to be spherical, the possible variability of the particle shape is increased dramatically, and can range from spheres over spheroids and cubes to highly irregular particles (Cheng, 1980). Thus, if the shape of particles will be taken into account for general modeling of the optical parameters, it is necessary to decide for simplifications. Moreover, a model is necessary that allows one to consider reasonable shapes of non-spherical particles. In this paper the non-spherical mineral particles are approximated as spheroids, since this substantially improves the agreement between modeled and measured optical properties (Mishchenko et al., 1997; Kahnert et al., 2005) and an appropriate theory exists, the T-matrix method (TMM) (Waterman, 1971).

In the new version of OPAC the optical properties of the mineral components are modeled as spheroids with the TMM code provided by Mishchenko and Travis (1998), with the aspect ratio distributions of the used spheroids varied with the particle size, as found by electron microscope investigations. The other microphysical properties of the components, the size distribution and the spectral refractive indices, have not been changed against the old OPAC. During the Saharan Mineral Dust Experiment field campaign (SAMUM-1), which was located close to the Sahara and its mineral sources and used a lot of different aerosol measurement systems (Heintzenberg, 2009), desert aerosol size distributions have been measured both in situ on an airplane (Weinzierl et al., 2009) and inferred by the AERONET (Aerosol Robotic Network) inversion algorithm from ground-based photometer measurements. The results differ considerably (Müller et al., 2010), but the OPAC size distributions are in-between. Moreover, photometer measurements in the solar aureole (where the non-sphericity has no influence) and values modeled with OPAC type “desert” agree very well (Gasteiger, 2011). Also, optical properties of Saharan dust measured by aircraft in 1999 compare very favorably with OPAC results (Haywood et al., 2001) for radiative properties that are independent of the scattering angle, like asymmetry parameter, single scattering albedo, and specific extinction coefficient, for which the non-sphericity has negligible influence. Thus, the OPAC size distributions for desert aerosol are assumed to be adequate for a combination with the information on particle shape from SAMUM.

Also not changed against the old OPAC is the possibility of the flexible mixing of the components and of the outcome of OPAC, like optical properties depending on relative humidity and available for a large wavelength range. In the new version of OPAC (4.0), which is freely available for non-commercial use, the optical properties modeled for non-spherical mineral particles are taken into account directly for practical application.

The effects of the particle shape are different for different optical properties which is shown in this paragraph for a variation of the optical properties available from OPAC. Examples are presented for the deviations between optical properties caused by mineral particles that are assumed as spheres and those assumed as spheroids with the aspect ratio distributions after Kandler C.

The phase function is very important for remote-sensing of desert aerosol and for its radiative forcing, and moreover, as mentioned above, for this optical quantity the effect due to non-sphericity is large, especially in the solar spectral range.

Thus, Fig. 2a shows the phase function for the two particle shape assumptions, for the mixture “desert” (Hess et al., 1998) and for different wavelengths. The assumed shape variation (spherical or non-spherical) is modeled only for the mineral particles: MINM 269.5 cm-3; MIAM 30.5 cm-3, MICM 0.142 cm-3. The 2000 cm-3 WASO are always assumed as spherical.

The phase functions show the known strong forward peak of aerosol particles, which is not influenced by the particle shape. It is increasing with increasing size parameter, and thus decreasing with wavelength. The particle shape effect is to be seen clearly in Fig. 2a in the backward scattering region, but more pronounced in Fig. 2b, where the belonging percentage deviations between the phase functions for particles with size dependent aspect ratio distributions and for spherical particles are shown.

The effect of the particle shape is up to almost +60 % at scattering angles around 130∘ and -60 % around 170∘ in the backscatter region. The effect decreases with increasing wavelength and is nearly negligible at 10 µm, as also shown. The reason is that the shape properties of the particles become less relevant if the wavelength of the radiation becomes larger relative to the particle size. In contrary, the effect of the particle shape is relatively low at 350 nm, but this results from the strong absorption of the mineral particles at this wavelength, which reduces the scattering effects in general and thus is dominant in comparison to the shape effect. The effect of the particle shape is strongest in the solar wavelength range, which is often used for aerosol remote-sensing and which is essential for radiative forcing and thus for climate effects. This documents again the need to take the non-spherical shape of mineral particles into account for remote-sensing or climate studies.

As mentioned, the aspect ratio distribution depends on the particle size. Thus, size distributions with different amounts of small and large particles may result in different variations of the phase function compared to that under the assumption of spheres. Since the life time of big particles in the atmosphere is less than that of smaller particles, in a dust storm not only the total amount of mineral particles in the air is high, but also the relative amount of large particles. During the transport, i.e. the time after the dust generation, the particle amount will be reduced due to sedimentation, but this effect can be stronger for larger particles. Finally, for background conditions, the total amount of mineral particles is low, and has the lowest amount of large particles (d'Almeida, 1987; Longtin et al., 1988; Tanré et al., 1988). The relative increasing amount of large particles with increasing turbidity that we assume to test the effect of non-sphericity with respect to particle size distribution is shown in Eqs. (2)–(4) (d'Almeida, 1987; Koepke et al., 1997). Given are correlations between the total number of mineral dust particles and the belonging numbers for the three mineral components. ln⁡NMINM=0.104+0.963ln⁡Nmineralln⁡NMIAM=-3.94+1.29ln⁡Nmineralln⁡NMICM=-13.7+2.06ln⁡Nmineral In Fig.  3, for desert aerosol with different turbidity, implemented with different total particle numbers, resulting in a different number of particles of the three mineral components, the phase functions for non-spherical desert particles are shown. Nmineral gives the total number of mineral particles. Nmineral = 75 stands for “background desert” conditions, Nmineral = 300 for average “desert” and Nmineral = 1200 for “dust storm”. It can be seen that the general effect of the non-spherical particle shape is always given, but does not differ considerably for the different size distributions, as a result of different total particle numbers. The effect of varying size distribution is more pronounced in the forward peak and the sideward scattering.

As mentioned, the WASO particles are spheres, with the consequence that the variation of their amount changes the phase function of the mixture. This is shown in Fig. 4 for “desert” with different amounts of WASO on the one hand, and for an average amount of 2000 WASO particles, but in combination with mineral particles for “background” and for “dust storm” conditions on the other hand.

Figure 4 shows that the effects due to the particle shape increase from background over desert to dust storm if the number of WASO is fixed, simply due to the increasing amount of non-spherical mineral particles. On the contrary, the effect due to non-spherical shape is reduced, to be seen for the type “desert”, if the amount of spherical WASO particles is increased. But it should be mentioned that the effect due to doubling or omitting WASO for the relative deviations of the phase function is less than the effect due to the variation of the amount of the mineral particles.

For the determination of the height dependent aerosol extinction coefficients, often backscatter lidar systems or ceilometers are used, because they are cheaper than higher sophisticated lidar instruments (Mona et al., 2012; Wiegner et al., 2014). However, for these instruments the measured signal is a result of both the extinction coefficient and the phase function at 180∘. Thus, to get the interesting height dependent extinction coefficient, it is necessary to use a quantity “lidar ratio”, which depends on the phase function and thus on the particle shape.

Figure 5 shows the lidar ratio for the aerosol type “desert”, both under the assumption of non-spherical and spherical mineral particles. The values are given for a wavelength range up to 40 µm, although no lidar instruments are available for wavelength larger ≈ 2 µm. Moreover, for the large wavelengths, the particles behave more and more like spheres, as already seen in Fig. 2b. For the interesting wavelength range around and below 1 µm, however, the consideration of non-sphericity is essential. With respect to independently measured lidar ratios, the agreement with modeled values is much better under the assumption of spheroids than of spheres (Gobbi et al., 2002). The lidar ratios to be seen in Fig. 5 are in good agreement with measured values from SAMUM (Groß et al., 2011). This is also generally valid for all lidar-wavelengths that have been used during SAMUM, but here the agreement between measured and modeled lidar ratios was reduced for the wavelength 355 nm, probably due to wrong assumptions with respect to the refractive index (Wiegner et al., 2009).

Optical quantities that are independent of the scattering angle or given as ratio between wavelengths are expected to be less sensitive with respect to the particle shape. To investigate this aspect, in Fig. 6 relative differences between spherical and non-spherical desert particles are presented for the spectral scattering-, absorption- and extinction-coefficients and for the asymmetry parameter. For all these quantities the deviations are less than 6 % and even less than 4 % in the part of the solar spectrum that is most relevant for climate effects. The same low dependency on the particle shape also holds for the single scattering albedo and the Ångström coefficient, not shown in a figure.

The main improvement of the new version of OPAC is the consideration of the non-sphericity of mineral particles. In OPAC for all optical quantities the large wavelength range between 0.25 and 40 µm is respected, with the consequence that the improved particle shape of mineral particles works both in the solar and in the infrared spectral region. Additionally, new in OPAC (4.0) is the possibility to model the particle mass for different cut-off radii, e.g. as used for PM10. On the other hand, the component “mineral-transported”, MITR, is no longer considered. This component had been used to describe desert aerosol under very remote conditions, as part of aerosol in polar regions. However, the amount of mineral dust particles should be reduced continuously on its way from the source, depending on their life time. This is possible with the remaining mineral components (e.g. using Eqs. 2–4), instead of switching to MITR. Thus, the aerosol type “Antarctic” in OPAC has been modified.

As discussed in the paper, the shape of the mineral particles has been improved. To avoid mistakes, the new mineral components are named in the new OPAC version with an N at the end, standing for non-spherical. The change from spheres to spheroids was made on the basis of cross section equivalence, resulting in a small reduction of the particle volume and thus the particle mass, resulting in the reduction factors shown in Table 3.

All the other microphysical aerosol properties are unchanged against the previous version of OPAC. Also the new version of OPAC gives the possibility to combine different aerosol components, in each case with individually decided particle number density for each component.

Results of OPAC (4.0) are a large number of optical properties (like phase function, scattering- absorption- and extinction coefficient, asymmetry parameter, single scattering albedo, Ångström coefficient, lidar ratio and visibility) and particle mass per volume. All properties can be modeled for different relative humidity and the optical properties are available as spectral values for the wide wavelength range of 0.25 to 40 µm and spectrally weighted for the solar and terrestrial range. For non-commercial use OPAC (4.0) is freely available at www.rascin.net.

Aerosol particles are one of the main gaps in the present knowledge of radiative forcing (Myhre et al., 2013), and mineral particles are especially essential due to their large amount and temporal and spatial variability. Since mineral particles in general are not spheres, Mie theory may lead to wrong values, both, if their optical properties are modeled based on size distribution and refractive index, and if remote-sensing data are used to get aerosol properties. Thus, the optical properties of mineral particles in the new version of OPAC are derived using TMM for spheroids. As described in this paper the non-sphericity is given by typical size dependent aspect ratio distributions of spheroids, which have been derived from measurements at observation campaigns. The predefined components in OPAC, now also for non-spherical mineral particles, are a big convenience, because users do not need to decide for individual single particle properties, as available from various studies and databases (Nousiainen, 2009; Meng et al., 2010).

The differences between spherical and non-spherical mineral particles are shown for a wide range of optical properties of desert aerosols. They are small, nearly negligible in the case of angular-independent optical quantities, like extinction-, scattering- and absorption-coefficients, asymmetry factor, single scattering albedo, and Ångström coefficient. However, the differences between spherical and non-spherical particles are large, up to 60 %, in the sideward and backward scattering regions of the phase functions in the solar spectral range. As a consequence, the deviations are also large in the lidar ratio, a parameter required to get height dependent extinction values from often used backscatter lidar measurements. The effect of the particle shape decreases with wavelength, since at wavelengths that are rather large with respect to the particle size, the particle shape is of less relevance.

It should be born in mind that the size distribution and the complex refractive index of the aerosol particles are very important for their optical properties. For the radiative properties in the thermal infrared the uncertainty in the refractive index will outperform the shape effect, which moreover depends on the absorption of the particles (Legrand et al., 2014). However, in this article only the aspect of the shape of mineral particle is discussed, and in the new version of OPAC the shape of the mineral particles has been improved, but the assumed size distributions and spectral refractive indices have not been changed. This will be done in the future, where it is planned also to add a stronger absorbing mineral component that allows for a larger variability of mixtures to describe desert aerosol.

Since the solar spectral range is often used for remote-sensing of aerosol particles and relevant for aerosol radiative forcing, the consideration of the phase functions of non-spherical mineral particles is a real improvement of OPAC, now available as version 4.0.