Michael Kahnert

Reproducing the optical properties of fine desert dust aerosols using ensembles of simple model particles

Abstract Single scattering optical properties are calculated for a proxy of fine dust aerosols at a wavelength of 0.55 μm . Spherical and spheroidal model particles are employed to fit the aerosol optical properties and to retrieve information about the physical parameters characterising the aerosols. It is found that spherical particles are capable of reproducing the scalar optical properties and the forward peak of the phase function of the dust aerosols. The effective size parameter of the aerosol ensemble is retrieved with high accuracy by using spherical model particles. Significant improvements are achieved by using spheroidal model particles. The aerosol phase function and the other diagonal elements of the Stokes scattering matrix can be fitted with high accuracy, whereas the off-diagonal elements are poorly reproduced. More elongated prolate and more flattened oblate spheroids contribute disproportionately strongly to the optimised shape distribution of the model particles and appear to be particularly useful for achieving a good fit of the scattering matrix. However, the clear discrepancies between the shape distribution of the aerosols and the shape distribution of the spheroidal model particles suggest that the possibilities of extracting shape information from optical observations are rather limited.

Variational data analysis of aerosol species in a regional CTM: background error covariance constraint and aerosol optical observation operators

A multivariate variational data assimilation scheme for the Multiple-scale Atmospheric Transport and CHemistry (MATCH) model is presented and tested. A spectral, non-separable approach is chosen for modelling the background error constraints. Three different methods are employed for estimating background error covariances, and their analysis performances are compared. Observation operators for aerosol optical parameters are presented for externally mixed particles. The assimilation algorithm is tested in conjunction with different background error covariance matrices by analysing lidar observations of aerosol backscattering coefficient. The assimilation algorithm is shown to produce analysis increments that are consistent with the applied background error statistics. Secondary aerosol species show no signs of chemical relaxation processes in sequential assimilation of lidar observations, thus indicating that the data analysis result is well balanced. However, both primary and secondary aerosol species display emission- and advection-induced relaxations.

Optical properties of light absorbing carbon aggregates mixed with sulfate: assessment of different model geometries for climate forcing calculations

Light scattering by light absorbing carbon (LAC) aggregates encapsulated into sulfate shells is computed by use of the discrete dipole method. Computations are performed for a UV, visible, and IR wavelength, different particle sizes, and volume fractions. Reference computations are compared to three classes of simplified model particles that have been proposed for climate modeling purposes. Neither model matches the reference results sufficiently well. Remarkably, more realistic core-shell geometries fall behind homogeneous mixture models. An extended model based on a core-shell-shell geometry is proposed and tested. Good agreement is found for total optical cross sections and the asymmetry parameter.

Models for integrated and differential scattering optical properties of encapsulated light absorbing carbon aggregates

Optical properties of light absorbing carbon (LAC) aggregates encapsulated in a shell of sulfate are computed for realistic model geometries based on field measurements. Computations are performed for wavelengths from the UV-C to the mid-IR. Both climate- and remote sensing-relevant optical properties are considered. The results are compared to commonly used simplified model geometries, none of which gives a realistic representation of the distribution of the LAC mass within the host material and, as a consequence, fail to predict the optical properties accurately. A new core-gray shell model is introduced, which accurately reproduces the size- and wavelength dependence of the integrated and differential optical properties.

Irreducible representations of finite groups in the T-matrix formulation of the electromagnetic scattering problem.

For particles with discrete geometrical symmetries, a group-theoretical method is presented for transforming the matrix quantities in the T-matrix description of the electromagnetic scattering problem from the reducible basis of vector spherical wave functions into a new basis in which all matrix quantities become block diagonal. The notorious ill-conditioning problems in the inversion of the Q matrix are thus considerably alleviated, and the matrix inversion becomes numerically more expedient. The method can be applied to any point group. For the specific example of the D6h group, it is demonstrated that computations in the new basis are faster by a factor of 3.6 as compared with computations that use the reducible basis. Most importantly, the method is capable of extending the range of size parameters for which convergent results can be obtained by 50%.

On the Discrepancy between Modeled and Measured Mass Absorption Cross Sections of Light Absorbing Carbon Aerosols

Recent modeling studies based on the Rayleigh-Debye-Gans (RDG) approximation have revealed a discrepancy between modeled and measured mass absorption cross sections (MAC) for atmospheric light absorbing carbon (LAC) aerosols. One plausible explanation is that this discrepancy is due to errors introduced by neglecting electromagnetic interactions among monomers in LAC aggregates within the RDG approximation. Here we compute MAC by use of numerically exact solutions to Maxwells equations and investigate the sensitivity of the results to a variation in the aggregates’ physical properties and refractive index. The results do confirm that approximate methods can introduce large errors in the results for the optical properties. However, these errors alone cannot explain the discrepancy between measured and modeled values of MAC. An agreement between observations and theoretical results can only be attained when assuming a fairly high value of the real and imaginary parts of the refractive index along the void-fraction curve and a mass density not exceeding 1.5–1.7 g/cm3.

Modeling optical properties of particles with small-scale surface roughness: combination of group theory with a perturbation approach

A T-matrix method for scattering by particles with small-scale surface roughness is presented. The method combines group theory with a perturbation expansion approach. Group theory is found to reduce CPU-time by 4-6 orders of magnitude. The perturbation expansion extends the range of size parameters by a factor of 5 compared to non-perturbative methods. An application to optically hard particles shows that small-scale surface roughness changes scattering in side- and backscattering directions, and it impacts the single-scattering albedo. This can have important implications for interpreting remote sensing observations, and for the climate impact of mineral aerosols.

Sensitivity of the shortwave radiative effect of dust on particle shape: Comparison of spheres and spheroids

The sensitivity of direct shortwave radiative effects of dust (DRE) to assumed particle shape is investigated. Radiative transfer simulations are conducted using optical properties of either spheres, mass-equivalent spheroids (mass-conserving case), or (mass-equivalent) spheroids whose number concentration is modified so that they have the same midvisible optical thickness (tau(545 nm)) as spheres (tau-conserving case). The impact of particle shape on DRE is investigated for different dust particle effective radii, optical thickness of the dust cloud, solar zenith angle, and spectral surface albedo (ocean, grass, and desert). It is found that the influence of particle shape on the DRE is strongest over ocean. It also depends very strongly on the shape distribution of spheroids used, to a degree that the results for two distributions of spheroids may deviate more from each other than from those for spheres. Finally, the effects of nonsphericity largely depend on whether the mass- or tau-conserving case is considered. For example, when using a shape distribution of spheroids recommended in a recent study for approximating the single-scattering properties of dust, the DRE at the surface differs at most 5% from that from spherical particles in the mass-conserving case. This stems from compensating nonsphericity effects on optical thickness, asymmetry parameter, and single-scattering albedo. However, in the tau-conserving case, the negative DRE at the surface can be up to 15% weaker for spheroids than spheres.

A case study on the reciprocity in light scattering computations

The fulfillment of the reciprocity by five publicly available scattering programs is investigated for a number of different particles. Reciprocity means that the source and the observation point of a given scattering configuration can be interchanged without changing the result. The programs under consideration are either implementations of T-matrix methods or of the discrete dipole approximation. Similarities and differences concerning their reciprocity behavior are discussed. In particular, it is investigated whether and under which conditions reciprocity tests can be used to evaluate the scattering results obtained by the different programs for the given particles.

SURFACE GREEN'S FUNCTION OF THE HELMHOLTZ EQUATION IN SPHERICAL COORDINATES

The surface Greens function belonging to the non-spheri- cal exterior boundary value problem of Helmholtzs equation in spher- ical coordinates is derived. This is performed in two ways, first by applying the Separation of Variables method, and, second, by using the Method of Lines as a special Finite-Difference technique. With this Greens function we are able to resolve some contradictions con- cerning conceptual aspects of the Separation of Variables method, the Finite-Difference methods, and the Boundary Integral Equation methods which have been developed for rigorously solving non-sepa- rable boundary value problems. The necessary mathematical back- ground, the relation to Watermans T matrix, and simplifications due to certain symmetry properties of the boundary surface will be discussed. In this paper we focus on the scalar problem. The extension to the vector case for electromagnetic wave scattering is in preparation and will be published later.