Franz Schreier

The Voigt and complex error function: A comparison of computational methods

Abstract Several computational procedures for the Voigt function and complex error function are discussed and compared with respect to accuracy and running time. Vectorization of the codes is applied where possible. Computational speed varied over two orders of magnitude. Even without vectorization, restructuring of the source code can yield a significant acceleration. The computational effort for Fourier transform methods is estimated and compared with other methods. For applications involving least-squares-fitting, the evaluation of the complex error function provides an efficient way to calculate both the Voigt function and its partial derivatives.

Intercomparison of general purpose clear sky atmospheric radiative transfer models for the millimeter/submillimeter spectral range

[1] We compare a number of radiative transfer models for atmospheric sounding in the millimeter and submillimeter wavelength range, check their consistency, and investigate their deviations from each other. This intercomparison deals with three different aspects of radiative transfer models: (1) the inherent physics of gaseous absorption lines and how they are modeled, (2) the calculation of absorption coefficients, and (3) the full calculation of radiative transfer for different geometries, i.e., up-looking, down-looking, and limblooking. The correctness and consistency of the implementations are tested by comparing calculations with predefined input such as spectroscopic data, line shape, continuum absorption model, and frequency grid. The absorption coefficients and brightness temperatures calculated by the different models are generally within about 1% of each other. Furthermore, the variability or uncertainty of the model results is estimated if (except for the atmospheric scenario) the input such as spectroscopic data, line shape, and continuum absorption model could be chosen freely. Here the models deviate from each other by about 10% around the center of major absorption lines. The main cause of such discrepancies is the variability of reported spectroscopic data for line absorption and of the continuum absorption model. Further possible causes of discrepancies are different frequency and pressure grids and differences in the corresponding interpolation routines, as well as differences in the line shape functions used, namely a prefactor of (n/n0 )o r (n/n0) 2 of the Van-Vleck-Weisskopf line shape function. Whether or not the discrepancies affect retrieval results remains to be investigated for each application individually.

Potential biosignatures in super-Earth atmospheres - I. Spectral appearance of super-Earths around M dwarfs

Atmospheric temperature and mixing ratio profiles of terres trial planets vary with the spectral energy flux distribution for di fferent types of M-dwarf stars and the planetary gravity. We investigate the resulting effects on the spectral appearance of molecular absorption bands, which are relevant as indicators for potential planetary habitability during primary and secondary eclipse for transiting terrestrial planets with Earth-like biomass emissi ons. Atmospheric profiles are computed using a plane-parallel, 1D climate model coupled with a chemistry model. We then calculate simulated spectra using a line-by-line radiative transfer model. We find that emission spectra during secondary eclipse show i ncreasing absorption of methane, water, and ozone for planets orbiting quiet M0-M3 dwarfs and the active M-type star AD Leo compared with solar-type central stars. However, for planets orbiting very cool and quiet M dwarfs (M4 to M7), increasing temperatures in the mid-atmosphere lead to reduced absorption signals, which impedes the detection of molecules in these scenarios. Transmission spectra during primary eclipse show strong absorption features of CH4, N2O and H2O for planets orbiting quiet M0-M7 stars and AD Leo. The N2O absorption of an Earth-sized planet orbiting a quiet M7 star can even be as strong as the CO2 signal. However, ozone absorption decreases for planets orbiting these cool central stars owing to chemical effects in the atmosphere. To investigate the effect on the spectroscopic detection of absorption bands with potential future satellite missions, we compute signal-to-noise-ratios (SNR) for a James Webb Space Telescope (JWST)-like aperture telescope.

A blind test retrieval experiment for infrared limb emission spectrometry

The functionality and characteristics of six different data processors (i.e., retrieval codes in their actual software and hardware environment) for analysis of high-resolution limb emission infrar ...

Numerical Regularization for Atmospheric Inverse Problems

The subject of this book is a hot topic with currently no monographic support. It is more advanced, specialized and mathematical than its competitors, and a comprehensive book on regularization techniques for atmospheric science is much needed for further development in this field. Written by brilliant mathematicians, this research monograph presents and analyzes numerical algorithms for atmospheric retrieval, pulling together all the relevant material in a consistent, very powerful manner. The first chapter presents the typical retrieval problems encountered in atmospheric remote sensing. Chapter 2 introduces the concept of ill-posedness for linear discrete equations, illustrating the difficulties associated with the solution of the problems by considering a temperature retrieval test problem and analyzing the solvability of the discrete equation by using the singular value decomposition of the corresponding matrix. A detailed description of the Tikhonov regularization for linear problems is the subject of Chapter 3, in which the authors introduce a set of mathematical and graphical tools to characterize the regularized solution. The goal of Chapter 4 is to reveal the similitude between Tikhonov regularization and statistical inversion regarding the regularized solution representation, the error analysis, and the design of parameter choice methods. The following chapter briefly surveys some classical iterative regularization methods such as the Landweber iteration and semi-iterative methods, and then treats the regularization effect of the conjugate gradient method applied to the normal equations. Having set the stage in the first part of the book, the remaining chapters dealing with nonlinear ill-posed problems. The authors introduce four test problems that are used throughout the rest of the book to illustrate the behaviour of the numerical algorithms and tools. These deal with the retrieval of ozone and BrO in the visible spectral region, and of CO and temperature in the infared spectral domain. Chapter 6 looks at the practical aspects of Tikhonov regularization for nonlinear problems, while Chapter 7 presents the relevant iterative regularization methods for nonlinear problems. The following chapter reviews the truncated and the regularized total least squares method for solving linear ill--posed problems, and include the similarity with the Tikhonov regularization. Chapter 9 brings the list of nonlinear methods to a close. It describes the Backus-Gilbert approach as a representative member of mollifier methods and finally, addresses the maximum entropy regularization. For the sake of completeness and in order to emphasize the mathematical techniques which are used in the classical regularization theory, five appendices at the end of the book present direct and iterative methods for solving linear and nonlinear ill-posed problems.

Robust and Efficient Inversion of Vertical Sounding Atmospheric High Resolution Spectra by Means of Regularization

Retrieval of atmospheric temperature or constituent profiles from vertical sounding spectroscopic measurements is an ill-posed problem, and additional information has to be introduced in the inversion process in order to compute meaningful solutions. Modern mathematical techniques are shown to be suitable for an analysis of these problems and the actual inversion to retrieve atmospheric profiles. A stable and efficient numerical implementation of Phillips-Tikhonov regularization techniques is discussed; generalized singular value decomposition is the appropriate tool to compute the formal solution of the modified minimization problem, and the L-curve permits determination of the optimum balance between information from measurement and side constraints. It is also shown that these techniques can provide further insight in the basic ill-posed nature of the inverse problem, give tools for the diagnostics of the retrieved profiles, and allow a discussion of the relation to other standard retrieval techniques, especially optimal estimation. The methods are demonstrated on examples for retrieval of ozone and hydroxyl profiles from simulated far infrared high-resolution spectra. A comparison with optimal estimation retrieval is performed by a preliminary analysis of a Spitsbergen millimeter-wave spectrum of ozone.

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.

Spectral features of Earth-like planets and their detectability at different orbital distances around F, G, and K-type stars

Context. In recent years, more and more transiting terrestrial extrasolar planets have been found. Spectroscopy already yielded the detection of molecular absorption bands in the atmospheres of Jupiter and Neptune-sized exoplanets. Detecting spectral features in the atmosphere of terrestrial planets is the next great challenge for exoplanet characterization. Aims. We investigate the spectral appearance of Earth-like exoplanets in the habitable zone (HZ) of different main sequence (F, G, and K-type) stars at different orbital distances. We furthermore discuss for which of these scenarios biomarker absorption bands and related compounds may be detected during primary or secondary transit with near-future telescopes and instruments. Methods. Atmospheric profiles from a 1D cloud-free atmospheric climate-photochemistry model were used to compute primary and secondary eclipse infrared spectra. The spectra were analyzed taking into account different filter bandpasses of two photometric instruments planned to be mounted to the James Webb Space Telescope (JWST). We analyzed in which filters and for which scenarios molecular absorption bands are detectable when using the space-borne JWST or the ground-based European Extremely Large Telescope (E-ELT). Results. Absorption bands of carbon dioxide (CO2), water (H2O), methane (CH4) and ozone (O3) are clearly visible in both highresolution spectra as well as in the filters of photometric instruments. However, only during primary eclipse absorption bands of CO2, H2 Oa nd O 3 are detectable for all scenarios when using photometric instruments and an E-ELT-like telescope setup. CH4 is only detectable at the outer HZ of the K-type star since here the atmospheric modeling results in very high abundances. Since the detectable CO2 and H2O absorption bands overlap, separate bands need to be observed to prove their existence in the planetary atmosphere. In order to detect H2O in a separate band, a ratio S /N > 7 needs to be achieved for E-ELT observations, e.g. by co-adding at least 10 transit observations. Using a space-borne telescope like the JWST enables the detection of CO2 at 4.3 μm, which is not possible for ground-based observations due to the Earth’s atmospheric absorption. Hence combining observations of space-borne and groundbased telescopes might allow to detect the presence of the biomarker molecule O3 and the related compounds H2 Oa nd CO 2 in a planetary atmosphere. Other absorption bands using the JWST can only be detected for much higher S/Ns, which is not achievable by just co-adding transit observations since this would be far beyond the planned mission time of JWST.

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.

Spectroscopic parameters for ozone and its isotopes: recent measurements, outstanding issues, and prospects for improvements to HITRAN

In this article we review ozone spectroscopy from the microwave to the ultraviolet since the release of the 1996 HITRAN database. Uncertainties, deficiencies, areas of potential improvement, and anticipated new spectral line parameters datasets are highlighted.