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 Landweber's 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.     

An efficient analytical approach for calculating line mixing in atmospheric remote sensing applications

Collisional coupling between energy states in a molecule undergoing an optical transition can alter the line shape associated with the transition, an effect known as line mixing. Accounting for this effect in the analysis of remote sensing measurements of Earth's atmosphere by the Atmospheric Chemistry Experiment (ACE) yields reduced residuals, which leads to improved performance in the volume mixing ratio retrievals for some molecules. Analytical expressions are presented for the imaginary components of the polynomial ratios from the Humlicek algorithm, which provides approximate solutions to the complex probability function. These imaginary components are employed in the calculation of line mixing using the Rosenkranz first order approximation. Examples of line mixing in ACE measurements are presented, including a set of CH₄ lines that exhibit both line mixing and speed dependence. An efficient, analytical approach is proposed for calculating line shapes with a combination of line mixing and speed dependence. FORTRAN routines for calculating line mixing effects are provided as a supplement to the paper.     

A comparison of regularization techniques for atmospheric trace gases retrievals

A comparison of regularization techniques aimed at maximizing the information content for atmospheric trace gas retrievals at an acceptable total error is presented. The total error of a retrieval is associated with the condition number of the regularized inverted matrix, which amplifies the measurement noise when moving from the measurement space to the state space as a noise error, and also together with the characteristics of the stabilizer, injects regularization error into the retrieval. Four different stabilizers: (i) the identity matrix, (ii) the first derivative operator, (iii) the second derivative operator, and (iv) the a-priori covariance matrix are used in this study to characterize the retrieval process under various regularization matrices using the regularized trust region method. For the cases simulated, it is found that the a-priori covariance matrix, which is used in traditional optimal estimation, and the identity matrix, which is used as a regularization in the Levenberg-Marquardt method, produce the highest total error, whereas the discrete one-dimensional Laplace first and second derivative operators produce the least total error at reasonably high information content.     

On the accuracy of covariance matrix: Hessian versus Gauss-Newton methods in atmospheric remote sensing with infrared spectroscopy

Most retrieval schemes use a linear approximation of the radiative transfer function within each iteration as well as for error analysis. Like most standard methods, the improved Hessian method relies on a quadratic form of the cost function and linear approximation in the error analysis. Often, there is no robust criterion in determining step size that can be used to calculate covariance matrix by discrete perturbation of the cost function in the Hessian approach. The Hessian method improved recently, however, overcomes this problem by employing adaptive algorithm which uses small step sizes in steep directions and large step sizes in flat directions of the cost function. The results of retrievals of atmospheric trace gases from simulated limb emission spectra show that Gauss-Newton algorithm and the improved Hessian generally give nearly identical volume mixing ratios and error covariance matrices in the original state vector space. Due to interlevel correlations, however, the agreement in the uncertainities in the original state vector coordinate system is partly lost in a space in which the elements of state vector are independent after orthogonal coordinate transformation. The significant discrepancies between the estimated uncertainities by the two methods are found to be related with elements of state vector that are dominantly controlled by flattest eigenvector directions of the inverse covariance matrix. The improved Hessian method determines the uncertainities in those shallowest directions with better accuracy than Gauss-Newton approach. The performance of the Hessian method is also found to be better in resolving structures related to the shallowest eigenvector directions as revealed by better vertical resolutions in the retrieved profiles of the trace species.     

O2A-band line parameters to support atmospheric remote sensing

Numerous satellite and ground-based remote sensing measurements rely on the ability to calculate O₂A-band [b¹Σ_g⁺←X³Σ_g⁻(0,0)] spectra from line parameters, with combined relative uncertainties below 0.5% required for the most demanding applications. In this work, we combine new ¹⁶O₂A-band R-branch measurements with our previous P-branch observations, both of which are based upon frequency-stabilized cavity ring-down spectroscopy. The combined set of data spans angular momentum quantum number, J′ up to 46. For these measurements, we quantify a J-dependent quadratic deviation from a standard model of the rotational distribution of the line intensities. We provide calculated transition wave numbers, and intensities for J′ up to 60. The calculated line intensities are derived from a weighted fit of the generalized model to an ensemble of data and agree with our measured values to within 0.1% on average, with a relative standard deviation of ≈0.3%. We identify an error in the calculated frequency dependence of the O₂A-band line intensities in existing spectroscopic databases. Other reported lineshape parameters include a revised set of ground-state energies, self- and air-pressure-broadening coefficients and self- and air-Dicke-narrowing coefficients. We also report a band-integrated intensity at 296 K of 2.231(7)×10⁻²² cm molec⁻¹ and Einstein-A coefficient of 0.0869(3) s⁻¹.     

O2A-band line parameters to support atmospheric remote sensing. Part II: The rare isotopologues

Frequency-stabilized cavity ring-down spectroscopy (FS-CRDS) was employed to measure over 100 transitions in the R-branch of the (0,0) band for the rare O₂ isotopologues. The use of ¹⁷O- and ¹⁸O-enriched mixtures allowed for line positions to be measured for the ¹⁶O¹⁷O, ¹⁶O¹⁸O, ¹⁷O₂, ¹⁷O¹⁸O, and ¹⁸O₂ isotopologues. Simultaneous fits to the upper and lower states were performed for each isotopologue using the FS-CRDS positions supplemented by microwave, millimeter, submillimeter, terahertz, and Raman ground state positions from the literature. Positions, line intensities, pressure broadening parameters, and collisional narrowing parameters are reported for the ¹⁶O¹⁸O and ¹⁶O¹⁷O isotopologues which are based upon the present study and our earlier FS-CRDS work (Long et al. J Quant Spectrosc Radiat Transfer 2010;111:2021 [18] and Robichaud et al. J Phys Chem A 2009;113:13089 [15]). The calculated line intensities include a term for the observed Herman-Wallis-like interaction and correct a frequency-dependent error, which is present in current spectroscopic databases.     

An empirical study on the importance of a speed-dependent Voigt line shape model for tropospheric water vapor profile remote sensing

We use high quality ground-based solar absorption spectra measured in close coincidence with Vaisala RS92 radiosonde in situ water vapor profiles to demonstrate that a Voigt line shape model yields systematic errors in the remotely sensed tropospheric water vapor profiles. We analyse absorption signatures of 4 H₂¹⁶O and 2 HD¹⁶O bands situated between 790 and 4710 cm⁻¹. We find that applying a speed-dependent Voigt line shape model instead of a Voigt line shape model significantly improves the agreement between the water vapor profiles obtained by the radiosondes and by infrared remote-sensing in the different bands. An optimal agreement is obtained for a Γ₂ (relaxation rate for speed-dependence) of 6-21% of Γ₀ (Voigt relaxation rate), which is consistent to the values derived from laboratory experiments. Our study suggests that further extensive laboratory investigations of line shape models are a key for improving the quality of modern water vapor remote sensing products.