Abstract. Insights are given into Tikhonov regularization and its application to the retrieval of vertical column densities of atmospheric trace gases from remote sensing measurements. The study builds upon the equivalence of the leastsquares profile-scaling approach and Tikhonov regularization method of the first kind with an infinite regularization strength. Here, the vertical profile is expressed relative to a reference profile. On the basis of this, we propose a new algorithm as an extension of the least-squares profile scaling which permits the calculation of total column averaging kernels on arbitrary vertical grids using an analytic expression. Moreover, we discuss the effective null space of the retrieval, which comprises those parts of a vertical trace gas distribution which cannot be inferred from the measurements. Numerically the algorithm can be implemented in a robust and efficient manner. In particular for operational data processing with challenging demands on processing time, the proposed inversion method in combination with highly efficient forward models is an asset. For demonstration purposes, we apply the algorithm to CO column retrieval from simulated measurements in the 2.3 µm spectral region and to O 3 column retrieval from the UV. These represent ideal measurements of a series of spaceborne spectrometers such as SCIA-MACHY, TROPOMI, GOME, and GOME-2. For both spectral ranges, we consider clear-sky and cloudy scenes where clouds are modelled as an elevated Lambertian surface. Here, the smoothing error for the clear-sky and cloudy atmosphere is significant and reaches several percent, depending on the reference profile which is used for scaling. This underlines the importance of the column averaging kernel for a proper interpretation of retrieved column densities. Furthermore, we show that the smoothing due to regularization can be underestimated by calculating the column averaging kernel on a too coarse vertical grid. For both retrievals, this effect becomes negligible for a vertical grid with 20-40 equally thick layers between 0 and 50 km.

Abstract. We present a sensitivity study of the direct fitting approach to retrieve total ozone columns from the clear sky Global Ozone Monitoring Experiment 2/MetOp-A (GOME-2/MetOp-A) measurements between 325 and 335 nm in the period 2007-2010. The direct fitting of the measurement is based on adjusting the scaling of a reference ozone profile and requires accurate simulation of GOME-2 radiances. In this context, we study the effect of three aspects that introduce forward model errors if not addressed appropriately:(1) the use of a clear sky model atmosphere in the radiative transfer demanding cloud filtering, (2) different approximations of Earth's sphericity to address the influence of the solar zenith angle, and (3) the need of polarization in radiative transfer modeling. We conclude that cloud filtering using the operational GOME-2 FRESCO (Fast Retrieval Scheme for Clouds from the Oxygen A band) cloud product, which is part of level 1B data, and the use of pseudo-spherical scalar radiative transfer is fully sufficient for the purpose of this retrieval. A validation with ground-based measurements at 36 stations confirms this showing a global mean bias of −0.1 % with a standard deviation (SD) of 2.7 %. The regularization effect inherent to the profile scaling approach is thoroughly characterized by the total column averaging kernel for each individual retrieval. It characterizes the effect of the particular choice of the ozone profile to be scaled by the inversion and is part of the retrieval product. Two different interpretations of the data product are possible: first, regarding the retrieval product as an estimate of the true column, a direct comparison of the retrieved column with total ozone columns from ground-based measurements can be done. This requires accurate a priori knowledge of the reference ozone profile and the column averaging kernel is not needed. Alternatively, the retrieval product can be interpreted as an effective column defined by the total column averaging kernel. This interpretation relies much less on the a priori knowledge of the reference ozone profile; however, for its validation, measurements of the vertical ozone distribution are needed. The different manners of data interpretation are demonstrated for simulated and real measurements using on-ground ozone column and ozonesonde measurements for validation.

[1] In this work we discuss the retrieval of ozone profiles from Infrared Atmospheric Sounding Interferometer (IASI) thermal infrared measurements in the presence of thin cirrus. An algorithm is presented which accounts for optically thin cirrus, described by an absorption layer at fixed altitude, where an effective cirrus optical depth is determined from IASI measurements at the 15 mm CO 2 absorption band. Subsequently, the cirrus characteristics are used for the ozone profile retrievals at the 9.6 mm O 3 absorption band. To retrieve ozone we employ a Tikhonov regularization scheme in combination with the L curve approach. A sensitivity study shows that neglecting thin cirrus in the ozone profile retrieval leads to errors of >20% in the troposphere for an infrared optical depth of <0.1 (t 550nm < 0.05), while errors are around 5% when accounting for thin cirrus in the proposed manner. Uncertainties on cirrus height are mostly compensated by the retrieval of the effective cloud parameter. The findings are confirmed when we apply the retrieval scheme to IASI measurements which are filtered according to water clouds and optically thick cirrus. The ozone profiles are validated with 193 collocated ozonesonde profiles from nine stations and show good improvement at all altitudes. For the different stations the differences in the mean profiles between IASI ozone profiles and sonde profiles at 5 km altitude improve from (−10)%-(+80)% when cirrus is not accounted for in the retrieval to (−10)%-(+35)% when employing the new retrieval scheme. At the same time the root-mean-square differences between IASI ozone profiles and sonde profiles improve from 30%-100% to 20%-50%.Citation: Wassmann, A., J. Landgraf, and I. Aben (2011), Ozone profiles from clear sky thermal infrared measurements of the Infrared Atmospheric Sounding Interferometer: A retrieval approach accounting for thin cirrus,

A concept is proposed to retrieve the vertical column densities of atmospheric trace gases from remote sensing measurements. It combines the numerical simplicity of a least-squares profile scaling retrieval with the numerically robust calculation of the total column averaging kernel using an analytic expression. The approach enables calculation of the total column averaging kernel on arbitrary vertical grids. Formally, the proposed method is equivalent to Tikhonov regularization of the first kind with an infinite regularization strength. Due to its efficiency it is particularly suited for implementation in operational data processing with high demands on processing time. To demonstrate the method, we apply it to CO column retrieval from simulated measurements in the 2.3 μm spectral region and to O₃ column retrieval from the UV, which represents ideal measurements of a series of space-borne spectrometers like SCIAMACHY, TROPOMI, GOME, and GOME-2. For both spectral ranges, we consider clear-sky and cloudy scenes where clouds are modelled as an elevated Lambertian surface. Here, the smoothing error for the clear-sky and cloudy atmosphere is significant and reaches several percent, depending on the reference profile which is used for scaling. This underlines the importance of the column averaging kernel for a proper interpretation of retrieved column densities. Furthermore, we show that the total column smoothing error is affected by a discretization error when total column averaging kernels are not represented on a fine enough vertical grid. For both retrievals this effect becomes negligible by using a vertical grid with 20–40 equally thick layers between 0 and 50 km

Abstract. In this work we present an extensive sensitivity study of retrieved total ozone columns from clear sky Global Ozone Monitoring Experiment 2 (GOME-2) measurements between 325 and 335nm which are corrected for instrument degradation. Employing an algorithm based on the scaling of a reference ozone profile with the extension to analytically calculate total column averaging kernels, allows us to investigate the impact of the choice of the reference profile on the retrieved total ozone column, since it represents a regularization of the retrieval. It introduces an error to the retrieved column with respect to the true column typically in the order of 1% depending on the reference scaling profile. However, a proper interpretation of the retrieved column using the total column averaging kernel avoids this error, which is demonstrated by a validation of GOME-2 total ozone columns with collocated ozonesonde and ground-based total ozone column measurements. Globally, we report a bias of 0.1% and a SD of 2.5% for 647 collocations with ground-based and ozonesonde measurements at different geolocations in the period of 2007 to 2010. Futhermore, an extended validation solely based on ground-based observations and a strict cloud filtering shows that the use of pseudo spherical scalar radiative transfer is fully sufficient for the purpose of this retrieval. Polarization of light by atmospheric scattering affects the retrieval accuracy only marginally and thus can be ignored. Finally, we study the effect of instrument degradation on the retrieved total ozone columns for the first four years of GOME-2 observations and discuss the efficiency of the proposed radiometric correction.