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Insights Into Tikhonov Regularization: Application to Trace Gas Column Retrieval and the Efficient Calculation of Total Column Averaging Kernels : Volume 7, Issue 2 (14/02/2014)

By Borsdorff, T.

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Book Id: WPLBN0003999580
Format Type: PDF Article :
File Size: Pages 13
Reproduction Date: 2015

Title: Insights Into Tikhonov Regularization: Application to Trace Gas Column Retrieval and the Efficient Calculation of Total Column Averaging Kernels : Volume 7, Issue 2 (14/02/2014)  
Author: Borsdorff, T.
Volume: Vol. 7, Issue 2
Language: English
Subject: Science, Atmospheric, Measurement
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Copernicus GmbH
Historic
Publication Date:
2014
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications

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Landgraf, J., Wassmann, A., Hasekamp, O. P., & Borsdorff, T. (2014). Insights Into Tikhonov Regularization: Application to Trace Gas Column Retrieval and the Efficient Calculation of Total Column Averaging Kernels : Volume 7, Issue 2 (14/02/2014). Retrieved from http://www.ebooklibrary.org/


Description
Description: SRON – Netherlands Institute for Space Research, Utrecht, the Netherlands. 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.

Summary
Insights into Tikhonov regularization: application to trace gas column retrieval and the efficient calculation of total column averaging kernels

Excerpt
Angelbratt, J., Mellqvist, J., Blumenstock, T., Borsdorff, T., Brohede, S., Duchatelet, P., Forster, F., Hase, F., Mahieu, E., Murtagh, D., Petersen, A. K., Schneider, M., Sussmann, R., and Urban, J.: A new method to detect long term trends of methane (CH4) and nitrous oxide (N2O) total columns measured within the NDACC ground-based high resolution solar FTIR network, Atmos. Chem. Phys., 11, 6167–6183, doi:10.5194/acp-11-6167-2011, 2011.; Barret, B., de Mazière, M., and Demoulin, P.: Retrieval and characterization of ozone profiles from solar infrared spectra at the Jungfraujoch, J. Geophys. Res., 107, 4788, doi:10.1029/2001JD001298, 2002.; Bhartia, P. K., McPeters, R. D., Flynn, L. E., Taylor, S., Kramarova, N. A., Frith, S., Fisher, B., and DeLand, M.: Solar Backscatter UV (SBUV) total ozone and profile algorithm, Atmos. Meas. Tech., 6, 2533–2548, doi:10.5194/amt-6-2533-2013, 2013.; Borsdorff, T. and Sussmann, R.: On seasonality of stratomesospheric CO above midlatitudes: New insight from solar FTIR spectrometry at Zugspitze and Garmisch, Geophys. Res. Lett., 36, L21804, doi:10.1029/2009GL040056, 2009.; Bovensmann, H., Burrows, J. P., Buchwitz, M., Frerick, J., Noël, S., Rozanov, V. V., Chance, K. V., and Goedec, A. P. H.: SCIAMACHY: Mission Objectives and Measurement Modes, J. Atmos. Sci., 56, 127–150, 1999.; Brion, J., Chakir, A., Daumont, D., Malicet, J., and Parisse, C.: High-resolution laboratory absorption cross section of O3, Temperature effect, Chem. Phys. Lett., 213, 610–612, doi:10.1016/0009-2614(93)89169-I, 1993.; Buchwitz, M. and Burrows, J. P.: Retrieval of CH4, CO and CO2 total column amounts from SCIAMACHY near-infrared nadir spectra: Retrieval algorithm and first results, Remote Sensing of Clouds and the Atmosphere VIII, Proc. SPIE, 5235, 375–388, 2004.; Burrows, J. P., Weber, M., Buchwitz, M., Rozanov, V., Ladstäter-Weißenmayer, A., Richter, A., DeBeek, R., Hoogen, R., Bramstedt, K., Eichmann, K. U., Eisinger, M., and Perner, D.: The global monitoring experiment (GOME): Mission concept and first scientific results, J. Atmos. Sci., 56, 151–175, 2.0.CO;2>doi:10.1175/1520-0469(1999)056<0151:TGOMEG>2.0.CO;2, 1999.; Butz, A., Guerlet, S., Hasekamp, O., Schepers, A. G., Aben, I., Frankenberg, C., Hartmann, J. M., Tran, H., Kuze, A., Keppel-Aleks, G. T., Wunch, D., Wennberg, P., Deutscher, N., Griffith, D., Macatangay, R., Messerschmidt, J., Notholt, J., and Warneke, T.: Toward accurate CO2 and CH4 observations from GOSAT, Geophys. Res. Lett., 38, L14812, doi:10.1029/2011GL047888, 2011.; Callies, J., Corpaccioli, E., Eisinger, M., Hahne, A., and Lefebvre, A.: GOME-2 – Metop's Second Generation Sensor for Operational Ozone Monitoring, ESA Bulletin, 102, ESTEC, Noordwijk, the Netherlands, 2000.; Eskes, H. J. and Boersma, K. F.: Averaging kernels for DOAS total-column satellite retrievals, Atmos. Chem. Phys., 3, 1285–1291, doi:10.5194/acp-3-1285-2003, 2003.; Eskes, H. J., van der A, R. J., Brinksma, E. J., Veefkind, J. P., de Haan, J. F., and Valks, P. J. M.: Retrieval and validation of ozone columns derived from measurements of SCIAMACHY on Envisat, Atmos. Chem. Phys. Discuss., 5, 4429–4475, doi:10.5194/acpd-5-4429-2005, 2005.; Frankenberg, C., Platt

 

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