Michael Hess

Iteratively Regularized Gauss--Newton Method for Atmospheric Remote Sensing

Abstract In this paper we present an inversion algorithm for nonlinear ill-posed problems arising in atmospheric remote sensing. The proposed method is the iteratively regularized Gauss–Newton method. The dependence of the performance and behaviour of the algorithm on the choice of the regularization matrices and sequences of regularization parameters is studied by means of simulations. A method for improving the accuracy of the solution when the identity matrix is used as regularization matrix is also discussed. Results are presented for atmospheric temperature retrievals from a far infrared spectrum observed by an airborne uplooking heterodyne instrument.

Iterative regularization methods for atmospheric remote sensing

In this paper we present different inversion algorithms for nonlinear ill-posed problems arising in atmosphere remote sensing. The proposed methods are Landwebers method (LwM), the iteratively regularized Gauss-Newton method, and the conventional and regularizing Levenberg-Marquardt method. In addition, some accelerated LwMs and a technique for smoothing the Levenberg-Marquardt solution are proposed. The numerical performance of the methods is studied by means of simulations. Results are presented for an inverse problem in atmospheric remote sensing, i.e., temperature sounding with an airborne uplooking high-resolution far-infrared spectrometer.

Cirrus optical thickness and crystal size retrieval from ATSR-2 data using phase functions of imperfect hexagonal ice crystals

Along Track Scanning Radiometer 2 (ATSR-2) measurements made over a tropical cirrus anvil are analyzed on the basis of radiative transfer calculations for clouds consisting of imperfect hexagonal ice crystals. Reflectivity measurements made at two wavelengths (0.87 μm, nonabsorbing; 1.6 μm, absorbing) and two viewing directions (nadir and forward) are considered. Model calculations for a cloud consisting of single-sized imperfect hexagonal ice crystals adequately explain the gross features of the ATSR-2 reflectivity measurements. Retrieved values of optical thickness and crystal size reveal no discernible relationship between these quantities. Nadir-derived and forward-derived optical thickness and crystal size are compared for both imperfect and near-perfect hexagonal crystals. For these two crystal shapes, there appears to be a moderate trade-off in consistent retrieval of crystal size versus retrieval of optical thickness. Consistent retrieval of crystal size is found for imperfect crystals. We find an average crystal size (defined as maximum crystal dimension) of 63±4 μm for a model cloud consisting of imperfect hexagonal columns. For imperfect hexagonal plates a somewhat larger value is retrieved: 71±3 μm. Both retrieved sizes suggest that the cloud system consisted of relatively small ice crystals.

Iteratively Regularized Gauss-Newton Method for Bound-Constraint Problems in Atmospheric Remote Sensing

In this paper two algorithms for the solution of nonlinear ill-posed problems with simple bounds on the variables are presented. The proposed algorithms are bound-constraint versions of the iteratively regularized Gauss-Newton method. The numerical performances of the algorithms are studied by means of simulations concerning the retrieval of molecular concentrations from limb sounding observations. For these examples, the unconstrained algorithm leads to unreasonable solutions.

Two software tools for plane-wave scattering on nonspherical particles in the German Aerospace Center’s virtual laboratory

We present the methodological background, the range of applicability, and the on-line usage of two software packages, MIESCHKA and CYL, which we have developed for light-scattering analysis on nonspherical particles. MIESCHKA solves Maxwells equations in a rigorous way but is restricted to axisymmetric geometries, whereas CYL is an approximation for finite columns with nonspherical cross sections. We have established an easy on-line access to both of these programs through the Virtual Laboratory. Its generic software infrastructure was designed to simplify the web-based usage and to support the intercomparability of scientific software.

Carbon Monoxide Vertical Column Density Retrieval from SCIAMACHY Infrared Nadir Observations

Nadir observations in the shortwave infrared channels of SCIAMACHY onboard the ENVISAT satellite can be used to derive information on CO, CH4, N2O, CO2, and H2O. BIRRA (Beer InfraRed Retriaval Algorithm) is a nonlinear least squares fit of the measured radiance: Trace gas vertical profiles are scaled to fit the observed data, further auxiliary parameters are code dependent. Here we discuss some features of the code and present results of carbon monoxide vertical column densities retrieved from SCIAMACHY infrared nadir observations.

Multi-parameter regularization method for atmospheric remote sensing

Abstract The iteratively regularized Gauss–Newton algorithm with simple bounds on the variables is extended to the multi-parameter case. The global regularization matrix is computed by using the L-curve method for a sequence of one-parameter regularization problems. Numerical results concerning the joint retrieval of O 3 and NO 2 profiles using the scattered light from the limb of the atmosphere are presented.

An iterative regularization method with B-spline approximation for atmospheric temperature and concentration retrievals

A retrieval algorithm using B-spline approximation for solving ill-posed inverse problems arising in atmospheric remote sensing is presented. The nonlinear ill-posed inversion is achieved by means of a hybrid approach combining higher-order B-spline functions and the iteratively regularized Gauss-Newton method. The performance of the inversion algorithm is studied by means of simulations for atmospheric temperature retrieval from far infrared airborne observations and molecular concentration retrievals from infrared limb emission spectra.

Nine years of atmospheric remote sensing with sciamachy - atmospheric parameters and data products

The SCIAMACHY instrument on-board ENVISAT measures since 2002 trace gas constituents of the atmosphere in nadir, limb and occultation configuration. It is an imaging spectrometer with q spectral range from the UV/VIS to SWIR (212 nm – 2384nm). In this paper we describe shortly the current status of the operational processing chains from Level 0-1b and Level 1b-2 that deliver Earth radiances, solar irradiance, trace gas total columns and profiles as well as cloud characteristics on an orbital basis. An outlook for future operational products is also given.

Correlations among the optical properties of cirrus-cloud particles: Microphysical interpretation: MICROPHYSICAL INTERPRETATION OF LIDAR DATA

Cirrus measurements obtained with a ground-based polarization Raman lidar at 67.9° N in January 1997 reveal a strong positive correlation between the particle optical properties, specifically depolarization ratio apar and extinction-to-backscatter (lidar) ratio Spar, for apar ~ 40%. Over the duration of the measurements both particle properties vary systematically. This effect is particularly pronounced in the case of apar which decreases significantly with time. The analysis of lidar humidity and radiosonde temperature data shows that the measured op- tical properties stem from scattering by dry solid ice particles, while scattering by supercooled droplets, or by wetted or subliming ice particles can be excluded. For the microphysical interpretation of the lidar measurements, ray-tracing computations of par~ticle scattering properties have been used. The comparison with the theoretical data sug- gests that the observed cirrus data can be interpreted in terms of size, shape, and growth of the cirrus particles, the latter under the assumption that the lidar measurements of consecutive cloud segments can be mapped on the temporal development of a single cloud parcel moving along its trajectory: Near the cloud top in the early stage of cirrus de- velopment, light scattering by nearly isometric particles that have the optical characteristics of hexagonal columns (short, column-like particles) is dominant. Over time the ice particles grow, and as the cloud base height extends to lower altitudes characterized by warmer temperatures they become morphologically diverse. For large Spar and depolarization values of ~ 40%, the scattering contributions of column- and plate-like parti- cles are roughly the same. In the lower ranges of the cirrus clouds, light scattering is pre- dominantly by plate-like ice particles. This interpretation assumes random orientation of the cirrus particles. Simulations with a simple model suggest, however, that the positive correlation between Spar and apar, which is observed for depolarization ratios < 40% mainly at low cloud altitudes, can be alternatively explained by horizontal alignment of a fraction of the cirrus particle population.