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| Titel |
Insights into Tikhonov regularization: application to trace gas column retrieval and the efficient calculation of total column averaging kernels |
| VerfasserIn |
T. Borsdorff, O. P. Hasekamp, A. Wassmann, J. Landgraf |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1867-1381
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| Digitales Dokument |
URL |
| Erschienen |
In: Atmospheric Measurement Techniques ; 7, no. 2 ; Nr. 7, no. 2 (2014-02-14), S.523-535 |
| Datensatznummer |
250115601
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| Publikation (Nr.) |
 copernicus.org/amt-7-523-2014.pdf |
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| Zusammenfassung |
| 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 least-squares 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 O3 column retrieval from the UV. These represent ideal
measurements of a series of spaceborne spectrometers such as
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 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. |
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