Mineral particles, in general, are not spheres and so the assumption
of spherical particles, instead of more realistic
shapes, has significant effects on modeled optical
properties and therefore on remote-sensing
procedures for desert aerosol and the derived radiative forcing. Thus, in a
new version of the database OPAC (Optical Properties of Aerosols and Clouds;
Hess et al., 1998), the optical properties of the mineral particles are
modeled describing the particles as spheroids with size dependent aspect
ratio distributions, but with the size distributions and the spectral
refractive indices not changed against the previous version of OPAC. The
spheroid assumption is known to substantially improve the scattering
functions but pays regard to the limited knowledge on particle shapes in an
actual case. The relative deviations of the optical properties of
non-spherical mineral particles from those of spherical particles are for the
phase function in the solar spectral range up to

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 most suitable method to model the optical properties of mineral aerosol
particles on a systematic basis (Wiegner et al., 2009) is TMM. It provides a solution of Maxwell's equations for the
interaction of radiation with arbitrarily-shaped particles (Waterman, 1971)
and is most efficient for rotationally symmetric particles. In our model the
mineral particles are given as spheroids, originating from rotation of
ellipses around one of their axes. Thus, an additional microphysical parameter
that has to be taken into account is the aspect ratio

For the results in this paper and the new version of OPAC, the
state-of-the-art TMM code from Mishchenko and Travis (1998) for randomly
oriented particles has been used for the mineral components. The T-matrix
calculations are supplemented by geometric optics calculations with the code
of Yang et al. (2007) for large particles not covered by the TMM code.
Wiegner et al. (2009) show the size coverage of the TMM code, which can model
dust spheroids up to size parameters,

This paper presents an improvement of OPAC, by modifying the shape of mineral particles. The other microphysical parameters used in OPAC, such as, the particle size distribution and the spectral refractive indices, have been left unchanged.

In OPAC the aerosol particles are given as components (Shettle and Fenn,
1979; Deepak and Gerber, 1983) resulting from an internal mixture of
particles of a certain origin. The particles of a component

The mineral dust is described in OPAC with three components as given in
Table 1: mineral nucleation mode (MINM), mineral accumulation mode (MIAM),
and mineral coarse mode (MICM), with

These mineral components can be mixed externally, also together with other components, to form individual aerosol types. In general, both over deserts and for other aerosol conditions with a dominant mass of mineral particles, water-soluble particles (WASO) are also present. These particles can be assumed to be spherical. Their amount is usually small with respect to their mass per volume, but since the particles are small their numbers per volume may be large.

In OPAC the aerosol type “desert” is a mixture of more than
200

Microphysical properties of mineral components.

The refractive indices of the components are wavelength-dependent (d'Almeida et al., 1991; Koepke et al., 1997). The particles of the mineral components all have the same refractive indices, since they are assumed to result from the same sources at the surface. The refractive index is given with an imaginary part that is responsible for the absorption properties of the particles.

To describe the shape properties of mineral particles of different size, for each of the three mineral components, the data of the “reference” case of SAMUM-1 have been used (Wiegner et al., 2009). The reference case was a situation with a very homogeneous desert aerosol layer up to 5 km above sea level which was very stable in time. The aspect ratio distribution of the particles was measured using electron microscopy and is given depending on particle size intervals by Kandler et al. (2009). For modeling the optical properties of mineral particles these wide aspect ratio distributions are applied to account for the large variety of the natural dust particle shapes. The belonging modeling results, compared to measured phase functions, are remarkably better than results when using only a single aspect ratio (Mishchenko et al., 1997; Nousiainen and Vermeulen, 2003). Moreover, all mineral particles are assumed to be prolate because this gives better agreement with measured scattering matrix elements of dust particles than using oblate or mixtures of prolate and oblate spheroids (Nousiainen and Vermeulen, 2003).

It is worth mentioning that the aspect ratio distribution of mineral particles did not vary significantly during SAMUM-1 and also not during the SAMUM-2 campaign, which was conducted further away from the dust source Sahara (Kandler et al., 2009, 2011). Thus, the selected aspect ratio distribution might be regarded as representative of Saharan dust.

The aspect ratio distributions depend on the size of the particles. For the
reference case the relative frequency of particles with a given aspect ratio
is available for 6 ranges of particle size (Kandler et al., 2009; Wiegner et
al., 2009). Some of them have similar aspect ratio distributions so that only
three radius ranges must be differentiated: for particles with

Aspect ratio distributions as function of particle radius interval
discretized from measurement data of Kandler et al. (2009). The first line covers
the measurement data from

Phase functions at 0.55

Each OPAC mineral component contains particles in all radius ranges given in
Table 2, with proportions that are varying according to the size distribution
of the components (Table 1). To check the shape effects, as a first test
(Kandler A) each mineral component is divided into the three radius ranges of
Table 2 and the belonging aspect ratio distribution of each range is applied.
This test is the most exact approach based on the available aspect ratio
data. As a second test – with respect to the idea of OPAC to keep things
easy – for all particles of each of the three OPAC mineral components a
fixed aspect ratio distribution has been used: the distribution of

As an example for the different considerations of the aspect ratio
distributions, in Fig. 1 the phase functions are shown under the assumption
of spherical particles and for non-spherical particles after the four tested
radius dependent aspect ratio distributions. The phase functions are given
for a wavelength 0.55

In Fig. 1 the increased sideward and reduced backward scattering is to be seen clearly which holds for all phase functions resulting from particles with non-spherical shape. The phase function after Dubovik is noticeably separated against those after Kandler A to C. But this result is not astonishing, since the direct electron microscopic investigations show that the aspect ratio distributions are size dependent, in contrast to the size-independent assumption by Dubovik. The phase functions after Kandler A (exact approach) and Kandler C are nearly identical, which means that the simpler assumptions in Kandler C give already correct results. Thus, for all optical property modeling of non-spherical mineral particles, both for the results shown in the following and for the new OPAC, the size dependent aspect ratio distribution after Kandler C is used.

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

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

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.

Phase functions of desert aerosol at 0.8

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.

Relative deviations (%) of phase functions at 0.55

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

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

Modeled values of the lidar ratio for “desert” aerosol under the assumption of spherical and non-spherical particles.

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

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

Deviation (%), between spherical and non-spherical “desert” aerosol for different optical quantities.

Reduction factors for particle volume and mass for the non-spherical mineral components, compared to the old components.

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

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.

This publication was partly funded by LMU Munich's Institutional Strategy LMUexcellent within the framework of the German Excellence Initiative. Edited by: P. Formenti