Stephan Havemann

Calculation of the single-scattering properties of randomly oriented hexagonal ice columns: a comparison of the T-matrix and the finite-difference time-domain methods.

We calculated the scattering and absorption properties of randomly oriented hexagonal ice columns using T-matrix theory, employing analytic orientation averaging, and the finite-difference time-domain method, which uses a numerical procedure to simulate random orientation. The total optical properties calculated are the extinction efficiency, absorption efficiency, single-scattering albedo, and the asymmetry parameter. The optical properties are calculated at the wavelengths of 0.66, 8.5, and 12 mum, up to a size parameter of 20 at 0.66 mum and 15 at the two other wavelengths. The phase-matrix elements P11, P12, and P22 are also calculated and compared, up to a size parameter of 20 at 0.66 mum and 15 at 12.0 mum. The scattering and absorption solutions obtained from the two independent electromagnetic methods are compared and contrasted, as well as the central processing unit time and memory load for each size parameter. It is found that the total optical properties calculated by the two methods are well within 3% of each other for all three wavelengths and size parameters. In terms of the phase-matrix elements it is found that there are some differences between the T-matrix and the finite-difference time-domain methods appearing in all three elements. Differences between the two methods for the P11 element are seen particularly at scattering angles from approximately 120 degrees to 180 degrees ; and at the scattering angle of 180 degrees , relative differences are less than 16%. At scattering angles less than 100 degrees , agreement is generally within a few percent. Similar results are also found for the P12 and P22 elements of the phase matrix. The validity of approximating randomly oriented hexagonal ice columns by randomly oriented equal surface area circular cylinders is also investigated in terms of the linear depolarization ratio.

Rapid computation of the optical properties of hexagonal columns using complex angular momentum theory

Abstract Asymptotic approximations to the Mie absorption and extinction efficiency factors have previously been derived from complex-angular-momentum theory. In this paper adjustments are made to the complex-angular-momentum absorption efficiency, based on the equivalent volume-to-area sphere, so that the asymptotic approximation can be applied to other particle shapes. Results are presented for randomly oriented finite-hexagonal ice columns in the infrared, comparing adjusted complex-angular-momentum theory to absorption solutions obtained from ray-tracing and Discretised-Mie-Formalism. The adjusted complex-angular-momentum absorption efficiencies and single scattering albedos are within 3% of the ray-tracing results. In the resonance region the adjusted complex-angular-momentum absorption efficiency is within 6% of the Discretised-Mie-Formalism results. The advantages of adjusted complex-angular-momentum theory are its speed compared to Discretised-Mie-Formalism and the ability to directly compare terms with geometric optics. The study of adjusted complex-angular-momentum suggests that phenomena often referred to as “tunnelling” are dependent on morphology as well as refractive index and size parameter. The dependence on morphology can be used to estimate the absorption efficiency at other infrared wavelengths. The analysis is also used to show the limits over which the anomalous diffraction approximation, often used in remote sensing retrievals of ice cloud properties, is a valid assumption.

A study of the absorption and extinction properties of hexagonal ice columns and plates in random and preferred orientation, using exact T-matrix theory and aircraft observations of cirrus

Abstract Absorption and extinction properties of the finite hexagonal ice column and hexagonal ice plate in random and preferred orientation are studied at the wavelength of 80 μm using a new implementation of exact T-matrix theory. For the case of random orientation at size parameters around two, it is shown that the hexagonal ice column and hexagonal ice plate absorption resonances are diminished relative to Mie theory, and the same behaviour is also noted for an aggregate particle consisting of eight hexagonal elements. The absorption properties of the aggregate particle have been calculated using the finite-difference time-domain method. It is also shown that extinction and absorption solutions for the hexagonal ice column and hexagonal ice plate can differ significantly if incidence occurs perpendicular or parallel to the cylindrical axis of the hexagon. For the case of perpendicular incidence on the edge of the hexagon, absorption solutions can exceed those of Mie theory, and for the case of parallel incidence, behaviour of the extinction solutions for hexagonal ice columns and hexagonal ice plates is shown to be similar to previously published work based on the prolate and oblate spheroid. Interference structure, associated with surface waves, is resolved on the hexagonal column extinction solution and the hexagonal plate absorption solution, thereby demonstrating that surface waves can exist on a non-axisymmetric geometry. The usefulness of assuming the hexagonal ice column in retrieval of ice crystal effective size is also investigated using aircraft based radiometric observations of semi-transparent cirrus at the wavelengths of 8.5 and 11 μm .

A consistent set of single-scattering properties for cirrus cloud: tests using radiance measurements from a dual-viewing multi-wavelength satellite-based instrument

Abstract In this paper a consistent set of single-scattering properties is presented for radiative transfer calculations and remote sensing of cirrus cloud. The single-scattering properties consist of the extinction coefficient, single-scattering albedo and phase function. A randomly oriented randomized hexagonal ice aggregate is assumed to derive the extinction coefficient and single-scattering albedo. The phase function is an extension of the Henyey–Greenstein model called the “analytic” phase function, which is generated from the asymmetry parameter at non-absorbing and absorbing wavelengths. The satellite-based dual-view along track scanning radiometer (ATSR-2) instrument is utilized to test the single-scattering properties for consistency at scattering angles between about 60° and 170°, using a method of Optimal Estimation. Optimal Estimation is applied to a set of cloud parameters and radiance measurements, which are made simultaneously at the wavelengths of 0.87, 1.6, 3.7, 11.0 and 12.0 μm , over cases of cirrus cloud located in the tropics and mid-latitudes. If the single-scattering properties and assumed model parameters were a perfect representation of the radiative properties of cirrus then the measurement residuals (i.e., differences between measurements and simulated measurements) would be identically equal to zero at each of the wavelengths for all scattering angles. It is found that the randomized ice aggregate combined with the analytic phase function minimizes the measurement residuals to generally well within ±1% (reflectance) and ±1 K (brightness temperature) at 0.87, 11.0 and 12.0 μm and to within ±3% and ±3 K at 1.6 and 3.7 μm , respectively. This compares to measurement residuals of about 8% and 10 K if the single-scattering properties are based on the randomly oriented hexagonal ice column. It is recommended that single-scattering properties based on the randomized ice aggregate combined with the analytic phase function (or a very similar phase function) should be applied to remote sensing and radiative transfer studies of cirrus cloud.

Photon tunneling contributions to extinction for laboratory grown hexagonal columns

Abstract A new treatment predicting the extinction and absorption properties of ice particles is evaluated in this study using laboratory measurements of the extinction efficiency, Q ext . In this treatment, the degree of ‘photon tunneling’ for ice crystals is unspecified, and laboratory measurements of Q ext were used in conjunction with this scheme to quantify the significance of this process by determining a tunneling factor, denoted t f . The term tunneling here refers to the interaction of a particle with radiation outside its area cross-section. A t f of 1.0 corresponds to tunneling exhibited by ice spheres as predicted by Mie theory, while a t f of 0 indicates no tunneling. The laboratory work entailed Fourier transform infrared spectroscopy (FTIR) for optical depth measurements in an ice cloud grown in a chamber, over a wavelength range of 2– 18 μm . From these measurements, the extinction efficiency Q ext as a function of wavelength was determined. Ice particle size spectra were measured in the cloud chamber, and were used to predict Q ext using the radiation scheme noted above and also using a new implementation of T-matrix, which is based on the exact geometry of a ‘pristine’ hexagonal ice crystal, without approximating the crystal as a spheroid. Results show that t f values determined from the laboratory measurements and the new radiation scheme are qualitatively in agreement with t f values based on fundamental theory. Mean Q ext errors (relative to measured Q ext ) over all wavelengths sampled were ⩽3.0% when using a constant optimized t f in the radiation scheme, and ⩽2.3% when using a t f scheme based on complex angular momentum theory. Moreover, Q ext as predicted from T-matrix over the wavelength interval 8– 12 μm is also in excellent agreement with the measured Q ext . A single wavelength calculation at 14 μm was performed using the finite difference time domain (FDTD) and T-matrix methods, both of which agreed precisely with the measured Q ext value. This validates the integrity of T-matrix, FDTD, the new radiation scheme, and the laboratory measurements for the corresponding range of wavelengths and size parameters. Collectively, these results indicate the tunneling contributions predicted for solid hexagonal columns are realistic.

Microphysical properties of mixed-phase & Ice clouds retrieved from In Situ airborne “polar nephelometer” measurements

In this paper we present microphysical properties of natural clouds retrieved from an airborne “Polar Nephelometer” measurements. The retrieval was done by means of an iterative inversion method, which is based on the bi-component (water droplets and ice crystals) representation of ice and mixed phase cloud composition. The present study shows that experimental scattering phase functions of ice crystals are characterized by high information content with respect to the aspect ratio of ice crystals which can be estimated in addition to their effective size distributions.

Light scattering on hexagonal ice columns

Light scattering on finite dielectric cylinders having noncircular cross sections has become of growing importance in remote-sensing applications. For analyzing their scattering characteristics at moderate size parameters, i.e., at a region where ray-tracing techniques fail, a few methods have been developed, among which an approximation based on the generalized separation-of-variables method has become very successful. This approach reveals two interesting features, which we discuss, that reduce the numerical effort drastically if applied to hexagonal (in general, 2n-periodic) boundary surfaces. Finally, some results for the phase function of hexagonal ice columns are given.

The development of a fast radiative transfer model based on an empirical orthogonal functions (EOF) technique

Remote sensing with the new generation of highly spectrally resolving instruments like the Atmospheric Research Interferometer Evaluation System (ARIES) or the assimilation of highly resolved spectra from satellites into Numerical Weather Prediction (NWP) systems requires radiative transfer computations that deliver results essentially instantaneous. This paper reports on the development of such a new fast radiative transfer model. The model is based on an Empirical Orthogonal Functions (EOF) technique. The model can be used for the simulation of sensors with different characteristics and in different spectral ranges from the solar to the infrared. For the purpose of airborne remote sensing, the fast model has been designed to work on any altitude and for slant paths whilst looking down or up. The fast model works for situations with diverse temperature and humidity profiles to an accuracy of better than 0.01K for most of the instrument channels. The EOF fast model works for clear-sky atmospheres and is applicable to atmospheres with scattering layers of aerosols or clouds. The fast model is trained with a large set of diverse atmospheric training profiles. In forward calculations corresponding high resolution spectra are obtained. An EOF analysis is performed on these spectra and only the leading EOF are retained (data compression). When the fast model is applied to a new independent profile, only the weights of the EOF need to be calculated (=predicted). Monochromatic radiances at suitable frequencies are used as predictors. The frequency selection is done by a cluster algorithm, which sorts frequencies with similar characteristics into clusters.

Implementation of the T-matrix method on a massively parallel machine: a comparison of hexagonal ice cylinder single-scattering properties using the T-matrix and improved geometric optics methods

Abstract This paper describes a series of improvements to an already existing T -matrix implementation for calculating the single-scattering properties of non-axisymmetric particles at large size parameters. The improvements aim to use the computational resources in terms of memory and time as efficiently as possible by taking into account various simplifications of the T -matrix formulation. In this paper, the randomly oriented hexagonal ice crystal is considered and the orientational averaging is done analytically. Within the framework of the T -matrix approach, symmetries of the hexagonal cylinders allow the formulation of eight independent subproblems, for each of which the memory demand is reduced by a factor of 144 compared to the general formulation. The memory demand strongly increases as a function of size parameter. For non-axisymmetric particles, memory demand rises approximately as the fourth power of the size parameter. In order to have more memory available, the T -matrix code was parallelized and implemented on a multi-processor CRAY T3E supercomputer. Extended precision is software emulated. With these new developments the single-scattering properties of randomly oriented hexagonal columns can be calculated for size parameters up to about 40. This size parameter reaches into the region of improved geometric optics (IGO), which is applicable down to size parameters of around 20. Comparisons of IGO and T -matrix results for the single-scattering albedo and the extinction efficiency show that at a size parameter of around 30, the single-scattering albedos are generally within about 2%. IGO underpredicts the extinction efficiency by 4% at λ=3.775 μm and by 11% at the more absorbing wavelength of λ=4.9 μm . This underprediction may be due to the version of IGO used since this does not take into account the inhomogeneity of the refracted wave in an absorbing medium.

SCATTERING OF PLANE WAVES ON FINITE CYLINDERS WITH NON-CIRCULAR CROSS-SECTIONS

A pillow including a top and bottom fibrous web defining a casing includes a radio mounted within the casing cooperating with a remotely located speaker. The pillow further includes the speaker mounted within a speaker housing, including fluid filled walls, and where the housing cavity includes compressible fluid capsules to accommodate impact to the speaker unit. The pillow structure may further be provided with a serpentine pneumatic chamber filled with further compressible fluid capsules to afford comfort and cushioning to a user, as well as components of the radio-clock system.