The spatiotemporal distribution and characterization of aerosol particles are usually determined by remote-sensing and optical in situ measurements. These measurements are indirect with respect to microphysical properties, and thus inversion techniques are required to determine the aerosol microphysics. Scattering theory provides the link between microphysical and optical properties; it is not only needed for such inversions but also for radiative budget calculations and climate modeling. However, optical modeling can be very time-consuming, in particular if nonspherical particles or complex ensembles are involved.

In this paper we present the MOPSMAP package (Modeled optical properties of ensembles of aerosol particles), which is computationally fast for optical modeling even in the case of complex aerosols. The package consists of a data set of pre-calculated optical properties of single aerosol particles, a Fortran program to calculate the properties of user-defined aerosol ensembles, and a user-friendly web interface for online calculations. Spheres, spheroids, and a small set of irregular particle shapes are considered over a wide range of sizes and refractive indices. MOPSMAP provides the fundamental optical properties assuming random particle orientation, including the scattering matrix for the selected wavelengths. Moreover, the output includes tables of frequently used properties such as the single-scattering albedo, the asymmetry parameter, or the lidar ratio. To demonstrate the wide range of possible MOPSMAP applications, a selection of examples is presented, e.g., dealing with hygroscopic growth, mixtures of absorbing and non-absorbing particles, the relevance of the size equivalence in the case of nonspherical particles, and the variability in volcanic ash microphysics.

The web interface is designed to be intuitive for expert and nonexpert users.
To support users a large set of default settings is available, e.g., several
wavelength-dependent refractive indices, climatologically representative size
distributions, and a parameterization of hygroscopic growth. Calculations are
possible for single wavelengths or user-defined sets (e.g., of specific
remote-sensing application). For expert users more options for the
microphysics are available. Plots for immediate visualization of the results
are shown. The complete output can be downloaded for further applications.
All input parameters and results are stored in the user's personal folder so
that calculations can easily be reproduced. The web interface is provided at

Scheme of the MOPSMAP package, including the optical modeling codes applied to create the data set.

Aerosol particles in the Earth's atmosphere are important in various ways,
for example because of their interaction with electromagnetic radiation and
their effect on cloud properties. Consequently aerosol particles are relevant
for weather and climate. The temporal and spatial variability in their
abundance as well as the variability in their properties is significant which
poses huge challenges in quantifying their effects. This includes the need to
establish extended networks of observations using instruments such as
photometers

Aerosol properties and distributions are often quantified by ground-based and spaceborne optical remote sensing and by optical in situ measurements. These measurements are indirect with respect to microphysical properties (e.g., particle size) because they measure optical quantities and require the application of inversion techniques to retrieve microphysical properties. Precise knowledge on the link between microphysical and optical properties is needed for the inversion. This link is provided by optical modeling, i.e., the optical properties of particles are calculated based on their microphysical properties. Optical modeling is required also for other applications, e.g., for radiative transfer, numerical weather prediction, and climate modeling. As optical modeling can be very time-consuming, it is often inevitable to pre-calculate optical properties of particles and store them in a lookup table, which is then accessed by the inversion procedures or subsequent models.

In our contribution we describe the MOPSMAP (Modeled optical properties
of ensembles of aerosol particles) package, which consists of a data
set of pre-calculated optical properties of single aerosol particles, a
Fortran program which calculates the properties of user-defined aerosol
ensembles from this data set, and a user-friendly web interface for online
calculations. Figure

In Sect. 2, after defining aerosol properties, we describe how existing
optical modeling codes were applied (green box in Fig.

The optical properties of a particle with known microphysical properties are calculated by optical modeling. For the creation of the basic data set of MOPSMAP, optical modeling of single particles has been performed. In this section, we first define microphysical and optical properties of single particles and then describe how we created the data set using existing optical modeling codes.

We emphasize that the data set is, in principle, applicable to the complete electromagnetic spectrum; however, we use, for simplicity, the term “light” and consequently “optics” instead of more general terms.

The description of particle properties is well-established and can be found in textbooks with varying levels of detail. Thus, we can restrict ourselves to a brief summary of those properties that are of special relevance for MOPSMAP.

The microphysical properties of an aerosol particle are described by its shape, size, and chemical composition.

Atmospheric aerosols might be spherical in shape but many types consist of
nonspherical particles, often with a large variety of different shapes.
Mineral dust

The size of a particle is commonly described by its radius or diameter. While
this is unambiguous in the case of spheres, more detailed specifications are
necessary for any kind of nonspherical particles. Often the size of an
equivalent sphere is used for the description of the nonspherical particle
size: the volume-equivalent radius

For setting up a data set of optical properties for different wavelengths, it
is highly beneficial to make use of the size parameter

The chemical composition of a particle determines its complex
wavelength-dependent refractive index

The optical properties of a nonspherical particle depend on the orientation
of the particle relative to the incident light. In our data set we assume
that particles are oriented randomly; thus, the optical properties are stored
as orientation averages

The orientation-averaged optical properties at a given wavelength are fully
described by the extinction cross section

For the scattering matrix

For many applications it is useful to expand the elements of the scattering
matrix using generalized spherical functions

The asymmetry parameter

Depending on the particle type, different approaches are available for
calculating particle optical properties. For the creation of the MOPSMAP
optical data set, we use the well-known Mie theory

We use the Mie code developed by

We use the extended precision version of the code described by

Optical properties of large spheroids were calculated with the improved
geometric optics method (IGOM) code provided by

Natural nonspherical aerosol particles, such as desert dust particles,
comprise practically an infinite number of particle shapes; thus, it is
impossible to cover the full range of shapes in aerosol models. Moreover, the
shape of each individual particle is never known under realistic atmospheric
conditions. Consequently, typical irregularities such as flat surfaces,
deformations or aggregation of particles can be considered only in an
approximating way. To enable the user of MOPSMAP to investigate the effects
of such irregularities the properties of six exemplary irregular particle
shapes, as introduced by

The optical properties were calculated with the discrete dipole approximation
code ADDA

Microphysics of spheres and spheroids considered in the MOPSMAP data set.

Microphysics of irregularly shaped particles considered in the MOPSMAP data set.

The computational demand of DDA calculations increases strongly with size
parameter

The ADDA code mainly allows the following code parameters to be optimized:

DDA formulation

stopping criterion of the iterative solver

number of dipoles per wavelength.

We estimate the accuracy of the ADDA results by comparing
orientation-averaged

The particle orientation is specified by three Euler angles
(

To test the accuracy of the selected orientation averaging scheme,
orientation-averaged optical properties for shapes B, C, D, and F were
compared to results using a much smaller step of 5

In summary, ADDA with the filtered coupled-dipole technique, at least 11
dipoles per wavelength and a stopping criterion for the iterative solver of

Using the codes with the settings described above, a data set of modeled
optical properties of single particles in random orientation was created. For
spheres, we stored averages over narrow size bins as described above instead of single particle properties. An overview over the wide range of
sizes, shapes, and refractive indices of the particles in the data set is
given in Tables

For spheres and spheroids the minimum size parameter is set to

The optical data for the irregularly shaped particles
(Table

The optical properties stored for each particle are the extinction efficiency

In the case of asymmetric shapes in random orientation, the scattering matrix has
10 independent elements as discussed by

Optical properties of single particles (or narrow size bins in the case
of spheres) with fixed refractive index

Figure

In this section the basic characteristics of the MOPSMAP Fortran program to
calculate optical properties of particle ensembles are described. Besides a
modern Fortran compiler, e.g., gfortran 6 or above, the netCDF Fortran
development source code is required to build the executable. The computation
time and memory requirements depend on the ensemble complexity and the number
of wavelengths but in general are low for state-of-the-art personal
computers. The Fortran code and the data set are available for download from

Simplified flow chart of the MOPSMAP Fortran program.

Within each MOPSMAP run the optical properties of a specific user-defined ensemble are calculated at a user-defined wavelength grid. The ensemble microphysics and the wavelength grid are defined in an input file. The details about the options available for the input file are described in a user manual which is provided together with the code.

Figure

Usually aerosol particles occur as ensembles of particles of different size,
refractive index, and/or shape. The different particles contribute to the
optical properties of the ensemble. Assuming that the distance between the
particles is large enough for interaction of light with each particle
to occur without influence from any other particle

In MOPSMAP particle ensembles are composed of one or more independent modes
(the terms “mode” and “component” are often used synonymously in the
literature). Each mode in MOPSMAP is characterized by particle size, shape,
and refractive index, whereby each property can be described as a fixed value
or as a distribution (see below). As these parameters do not necessarily
correspond to the grid points of the MOPSMAP data set, for each mode (and
each wavelength), decomposition into contributions from the different
available

For a mode containing spheroids, in the most simple but probably most
frequently used case of fixed values of

Under other conditions more or less than eight contributions have to be
considered. In the case of spheres or a single irregular shape, an interpolation
in the shape dimension is not necessary, so that four contributions are
sufficient. In the case of a spheroid aspect ratio distribution, contributions
from all required

The optical properties of the particle ensemble are calculated for each
wavelength by summation over extensive properties of all particles described
by the

The size distribution

The particle shape can be specified independently for each mode and is,
within each mode, independent of size and refractive index. In the case of
spheroids, either a fixed aspect ratio

The refractive index of each mode can either be wavelength-independent or
specified as a function of wavelength in an ASCII file. In addition, it is
possible to specify for each mode a non-absorbing fraction

For the hygroscopic particle growth the following parameterization

As output of MOPSMAP the following properties of aerosol ensemble are
available. Redundant properties, such as lidar-related properties, are
available to facilitate the use of the results:

extinction coefficient

single-scattering albedo

asymmetry parameter

effective radius

number density

cross section density

volume density

mass concentration

expansion coefficients (

scattering matrix elements (

volume scattering function

backscatter coefficient

lidar ratio

linear depolarization ratio

Ångström exponents

extinction-to-mass conversion factor

mass-to-backscatter conversion factor

Scattering matrix elements and the quantities derived from them are
calculated from the expansion coefficients. Wavelength-independent properties

The results are available in ASCII and in netCDF format. The format of the
program output is described in the user manual. The netCDF output files can
be read by the radiative transfer model uvspec, which is included in
libRadtran

Due to the limited size resolution in the data set and required
interpolations between refractive index and aspect ratio grid points,
deviations from exact model calculations for specific microphysical
properties occur. As examples, Fig.

Examples illustrating the effect of the limited size resolution of
the MOPSMAP data set

Optical properties calculated for a lognormal mode with

In Fig.

In Fig.

For other size ranges, refractive indices, and optical quantities, the effects on the single particle properties are in principle similar but they may vary in magnitude.

Table

The right half of Table

These comparisons demonstrate that deviations found for single particles are largely smoothed out in the case of particle ensembles due to the averaging over a large number of different particles. Only for a few special atmospheric applications, for example, the modeling of a rainbow, the limited resolution of the data set may still lead to a considerable error.

A web interface is provided as part of MOPSMAP at

Properties of OPAC aerosol types as a function of relative humidity RH
calculated with the

The output comprises the complete set of optical properties as described in
Sect.

All results are stored in the user's personal folder so that all calculations can be reproduced. Furthermore, all calculations can also easily be rerun with a slightly modified input parameter set.

In this section a selection of examples is presented to demonstrate the wide
range of applications of MOPSMAP. Many of them can be performed by using the
web interface. Some examples need a local version of MOPSMAP alongside with
scripts that repeatedly call the Fortran program. These scripts are written
in Python and can be downloaded from

It is worth mentioning that numerous studies demonstrate the need for optical
modeling of aerosol ensembles, thus illustrating the range of possible
applications of MOPSMAP. Moreover, optical modeling is essential for many
different related modeling activities. It is required, for example, for
closure experiments

The first example of applications deals with hygroscopic growth. If aerosol
particles are hygroscopic, their microphysical and optical properties change
with RH. Fig.

The upper row of Fig.

The single-scattering albedo

The extinction-to-mass conversion factor

The bottom row of Fig.

Currently the hygroscopic growth of different aerosol components is not
ultimately understood, and different

Aerosol transport models in combination with the optical properties of the
aerosol allow one to model the radiative effect of the aerosol. The aerosol
is typically modeled in terms of mass concentrations for a limited number of
aerosol types divided over a few size bins (sectional aerosol model) or a few
modes (modal aerosol models). Thus, realistic optical properties for each
size bin of each aerosol type are required for modeling the radiative effects

Optical properties at

In this example, we calculated the optical properties of dust at

The calculated phase functions are presented in Fig.

Phase functions at

Calculated parameters relevant for radiative transfer and remote sensing are
given in Table

Many in situ measurement setups are limited with respect to the maximum
particle size they are able to sample, e.g., because of losses at the inlet
or the tubing. In this example, we illustrate the effect of the cutoff for
the desert aerosol type from OPAC at RH

Properties of one-modal size distribution at

Optical and microphysical properties of the OPAC desert aerosol
type as a function of cutoff radius

Figure

This example shows that consideration of maximum size is essential when derived optical properties or mass concentrations are interpreted, and results can be severely misleading if the cutoff radius is not considered. These effects can be easily quantified with MOPSMAP and its web interface.

This example demonstrates how the selection of the size equivalence in the case
of nonspherical particles affects various ensemble properties. In MOPSMAP
the size-related parameters are either interpreted as

To further elucidate the role of the different representations of radii, the
same parameters of a lognormal size distribution are applied to the
different size interpretations. For this purpose, the parameters are set to

Lognormal size distributions (SD) with same

Since the size distributions depend on the selected size equivalence various
(optical) properties of the ensemble are also different; a quantification has
been provided by MOPSMAP (Table

The results are consistent with the increase in particle size from assuming

These results highlight the importance of a thoughtful selection of the size equivalence. The most appropriate size equivalence certainly depends on the concept of how the size distribution is measured. For example, if scattering by coarse dust particles is measured and the size is inverted assuming spherical particles, assuming cross-section equivalence in subsequent applications with nonspherical particles seems natural as scattering mainly depends on the particle cross section. MOPSMAP and its web interface provides the flexibility to investigate this topic theoretically.

In general, the knowledge on microphysical properties is limited; thus, they are subject to uncertainties. If these uncertainties can be quantified, it is consistent to also quantify the corresponding uncertainties of the optical properties.

In this regard, the sensitivity of a calculated optical property

Elements of the Jacobian matrix, i.e., first partial derivatives, of a dust-like ensemble (see text for details).

Table

The Jacobian matrix

Mineral dust aerosols are ensembles of different minerals with different
refractive indices. Usually the variability in the refractive index of the
particles within a dust aerosol ensemble is neglected when modeling its
optical properties. In this example, we compare optical properties calculated
using the full measured variability in the imaginary part of the refractive
index

We use the desert aerosol type of OPAC

Volume scattering function of dust at

Figure

These results emphasize that it is important to consider the nonuniform
distribution of the absorptive components in the desert dust ensembles for
optical modeling of such aerosols at short wavelengths. We have shown in this
example that optical properties of Saharan dust can be well simulated with

Integrating nephelometers aim to measure in situ the total scattering
coefficient

Modeled correction factors

Figure

The correction factors might be recalculated for example when new data on the
refractive index or particle shape become available. This example highlights
the potential of MOPSMAP as a useful tool for the characterization of optical
in situ instruments. In addition, it could be used for the interpretation of
angular measurements, for example, as performed with a polar photometer by

Modeled wavelength-dependent optical properties for
ashes from different volcanoes. More details on the ash samples are given in Table 1 of

Figure

This example suggests that it is worthwhile considering the specific microphysical properties of each volcano. However, for realistic MOPSMAP calculations valid in the long-range regime, size distributions different from the ones used in this example must certainly be applied whereas the refractive indices are more likely representative.

Radiative properties of atmospheric aerosols are relevant for a wide range of meteorological applications, in particular for radiative transfer calculations and remote-sensing and in situ techniques. Optical properties strongly depend on the microphysical properties of the particles – size, refractive index and shape – properties that are highly variable under ambient conditions. As a consequence, the application of mean properties could be questionable. However, the determination of optical properties of specific aerosol ensembles can be quite time-consuming, in particular when nonspherical particles shall be considered.

For this purpose we have developed the MOPSMAP package that provides the full
set of optical properties of arbitrary, randomly oriented aerosol ensembles:
single particles of the ensemble can be spherical or spheroidal with size
parameters up to

The details of the concept underlying MOPSMAP are discussed in this paper. Several examples are presented to illustrate the potential of the package, including an example to calculate optical properties for sectional aerosol models and an example illustrating the effect of maximum size cutoff that occurs in the inlet system of in situ instruments. In another example, conversion factors between the backscatter coefficient (available from lidar/ceilometer measurements or from numerical forecast models) and the mass concentration of volcanic ashes have been calculated. These conversion factors are relevant to estimate flight safety after volcanic eruptions and vary by about a factor of 3 between the nine ashes under investigation.

The concept of MOPSMAP allows continuous upgrades to further extend the range
of applications. For example, the resolution of the refractive index grid could be
increased, new versions of underlying scattering codes could be applied when
available, larger size parameters could be considered, e.g., using DDA for

The MOPSMAP data set and the Fortran code, including
scripts related to examples presented in this paper, are available at

JG set up the database of optical properties and implemented the Fortran codes; MW developed the web interface. The paper was written by both, with JG drafting the paper.

The authors declare that they have no conflict of interest.

This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement no. 640458, A-LIFE). The authors thank Michael Mishchenko, Ping Yang, and Maxim Yurkin for providing their optical modeling codes. Thanks are due to Daniel Sauer, Sara Valentini, Marilena Teri, and Bernadett Weinzierl for suggestions that helped to improve MOPSMAP. Edited by: Klaus Gierens Reviewed by: two anonymous referees