Atmospheric Chemistry and Physics
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7
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2007
10.5194/acp-7-397-2007
http://www.atmos-chem-phys.net/7/397/2007/
http://www.atmos-chem-phys.net/7/397/2007/acp-7-397-2007.html
http://www.atmos-chem-phys.net/7/397/2007/acp-7-397-2007.pdf
397
408
2007-01-23
Elimination of hidden a priori information from remotely sensed profile data
T. von Clarmann
thomas.clarmann@imk.fzk.de
U. Grabowski
Forschungszentrum Karlsruhe, Institut für Meteorologie und Klimaforschung, Karlsruhe, Germany
Profiles of atmospheric state variables retrieved from
remote measurements often contain a priori information
which causes complication in the statistical use of data
and in the comparison with other measured or modeled data.
For such applications it often is desirable to remove the
a priori information from the data product. If the retrieval
involves an ill-posed inversion problem, formal removal of
the a priori information requires resampling of the data
on a coarser grid, which in some sense, however, is a prior
constraint in itself. The fact that the trace of the averaging
kernel matrix of a retrieval is equivalent to the number of degrees
of freedom of the retrieval is used to define an appropriate
information-centered representation of the data where each
data point represents one degree of freedom. Since regridding
implies further degradation of the data and thus causes
additional loss of information, a re-regularization scheme
has been developed which allows resampling without
additional loss of information. For a typical ClONO<sub>2</sub>
profile retrieved from spectra as measured by the Michelson
Interferometer for Passive Atmospheric Sounding (MIPAS),
the constrained retrieval has 9.7 degrees of freedom.
After application of the proposed transformation to a coarser
information-centered altitude grid, there are exactly 9 degrees
of freedom left, and the averaging kernel on the coarse grid is
unity. Pure resampling on the information-centered grid without
re-regularization would reduce the degrees of freedom to 7.1 (6.7)
for a staircase (triangular) representation scheme.
Calisesi, Y., Soebijanta, V T., and van Oss, R.: Regridding of remote soundings: Formulation and application to ozone profile comparison, J. Geophys. Res., 110, D23306, doi:10.1029/2005JD006122, 2005.
Ceccherini, S., Carli, B., Pascale, E., Prosperi, M., Raspollini, P., and Dinelli, B M.: Comparison of measurements made with two different instruments of the same atmospheric vertical profile, Appl. Opt., 42, 6465–6473, 2003.
Endemann, M. and Fischer, H.: Envisat's High-Resolution Limb Sounder: MIPAS, ESA bulletin, 76, 47–52, 1993.
Esler, J G. and Waugh, D W.: A method for estimating the extent of denitrification of Arctic polar vortex air from tracer–tracer scatter plots, J. Geophys. Res., 107, 4169, doi:10.1029/2001JD001071, 2002.
Fischer, H. and Oelhaf, H.: Remote sensing of vertical profiles of atmospheric trace constituents with MIPAS limb-emission spectrometers, Appl. Opt., 35, 2787–2796, 1996. %
%Funke, B., López-Puertas, M., von Clarmann, T., Stiller, G P., Fischer, % H., Glatthor, N., Grabowski, U., Höpfner, M., Kellmann, S., Kiefer. M., % Linden, A., Mengistu Tsidu, G., Milz, M., Steck, T., and Wang, D. Y.: % Retrieval of stratospheric NO$_x$ from 5.3 and 6.2 μm nonlocal % thermodynamic equilibrium emissions measured by Michelson Interferometer % for Passive Atmospheric Sounding (MIPAS) on Envisat, J. Geophys. % Res., 110, D09302, doi:10.1029/2004JD005225", 2005.
Glatthor, N., von Clarmann, T., Fischer, H., Funke, B., Grabowski, U., Höpfner, M., Kellmann, S., Kiefer, M., Linden, A., Milz, M., Steck, T., Stiller, G P., Mengistu Tsidu, G., and Wang, D Y.: Mixing processes during the Antarctic vortex split in September/October 2002 as inferred from source gas and ozone distributions from ENVISAT-MIPAS, J. Atmos. Sci., 62, 787–800, 2005.
Höpfner, M., von Clarmann, T., Fischer, H., Glatthor, N., Grabowski, U., Kellmann, S., Kiefer, M., Linden, A., Mengistu Tsidu, G., Milz, M., Steck, T., Stiller, G P., Wang, D.-Y., and Funke, B.: First spaceborne observations of Antarctic stratospheric ClONO<sub>2</sub> recovery: Austral spring 2002, J. Geophys. Res., 109, D11308, doi:10.1029/2004JD005322, 2004.
Joiner, J. and da Silva, A M.: Efficient methods to assimilate remotely sensed data based on information content, Q. J. R. Meteorol. Soc., 124, 1669–1694, 1998.
Kondo, Y., Koike, M., Engel, A., Schmidt, U., Mueller, M., Sugita, T., Kanzawa, H., Nakazawa, T., Aoki, S., Irie, H., Toriyama, N., Suzuki, T., and Sasano, Y.: NO<sub>y</sub>–N<sub>2</sub>O correlation observed inside the Arctic vortex in February 1997: Dynamical and chemical effects, J. Geophys. Res., 104, 8215–8224, 1999.
Mengistu Tsidu, G., Stiller, G P., von Clarmann, T., Funke, B., Höpfner, M., Fischer, H., Glatthor, N., Grabowski, U., Kellmann, S., Kiefer, M., Linden, A., López-Puertas, M., Milz, M., Steck, T., and Wang, D Y.: NO<sub>y</sub> from Michelson Interferometer for Passive Atmospheric Sounding on Environmental Satellite during the Southern Hemisphere polar vortex split in September/October 2002, J. Geophys. Res., 110, D11301, doi:10.1029/2004JD005322, 2005.
Müller, R., Groß, J.-U., McKenna, D S., Crutzen, P J., Brühl, C., Russell III, J M., Gordley, L L., Burrows, J P., and Tuck, A F.: Chemical ozone loss in the Arctic vortex in the winter 1995–96: HALOE measurements in conjunction with other observations, Ann. Geophys., 17, 101–114, 1999.
Muscari, G., de~Zafra, R L., and Smyshlyaev, S.: Evolution of the NO<sub>y</sub>–N<sub>2</sub>O correlation in the Antarctic stratosphere during 1993 and 1995, J. Geophys. Res., 108, 4428, doi:10.1029/2002JD002871, 2003.
Nett, H., Carli, B., Carlotti, M., Dudhia, A., Fischer, H., Flaud, J.-M., Perron, G., Raspollini, P., and Ridolfi, M.: MIPAS Ground Processor and Data Products, in Proc. IEEE 1999 International Geoscience and Remote Sensing Symposium, 28 June–2 July 1999, Hamburg, Germany, 1692–1696, 1999.
Plumb, R A., Waugh, D W., and Chipperfield, M P.: The effects of mixing on tracer relationships in the polar vortices, J. Geophys. Res., 105, 10 047–10 062, 2000.
Ray, E A., Moore, F L., Elkins, J W., Hurst, D F., Romashkin, P A., Dutton, G S., and Fahey, D W.: Descent and mixing in the 1999–2000 northern polar vortex inferred from in situ tracer measurements, J. Geophys. Res., 107, 8285, doi:10.1029/2001JD000961, 2002.
Rex, M., von~der Gathen, P., Braathen, G O., Harris, N. R P., Reimer, E., Beck, A., Alfier, R., Krüger-Carstensen, R., Chipperfield, M., de~Backer, H., Balis, D., O'Connor, F., Dier, H., Dorokhov, V., Fast, H., Gamma, A., Gil, M., Kyrö, E., Litynska, Z., Mikkelsen, I S., Molyneux, M., Murphy, G., Reid, S J., Rummukainen, M., and Zerefos, C.: Chemical Ozone Loss in the Arctic Winter 1994/95 as determined by the Match Technique, Atmos. Environ., 32, 35–59, 1999.
Ridolfi, M., Carli, B., Carlotti, M., von Clarmann, T., Dinelli, B., Dudhia, A., Flaud, J.-M., Höpfner, M., Morris, P E., Raspollini, P., Stiller, G., and Wells, R J.: Optimized Forward and Retrieval Scheme for MIPAS Near-Real-Time Data Processing, Appl. Opt., 39, 1323–1340, 2000.
Rodgers, C D.: Inverse Methods for Atmospheric Sounding: Theory and Practice, vol 2 of Series on Atmospheric, Oceanic and Planetary Physics, edited by: Taylor, F. W., World Scientific, 2000.
Rodgers, C D. and Connor, B J.: Intercomparison of remote sounding instruments, J. Geophys. Res., 108, 4116, doi:10.1029/2002JD002299, 2003.
SAG: MIPAS, Michelson Interferometer for Passive Atmospheric Sounding, An ENVISAT Instrument for Atmospheric Chemistry and Climate Research, Scientific Objectives, Mission Concept and Feasibility, Instrument Design and Data Products, European Space Agency, 1999.
Steck, T.: Methods for determining regularization for atmospheric retrieval problems, Appl. Opt., 41, 1788–1797, 2002.
Steck, T. and von Clarmann, T.: Constrained profile retrieval applied to the observation mode of the Michelson Interferometer for Passive Atmospheric Sounding, Appl. Opt., 40, 3559–3571, 2001.
Stiller, G P. (Ed.): The Karlsruhe Optimized and Precise Radiative Transfer Algorithm (KOPRA), vol. FZKA 6487 of Wissenschaftliche Berichte, Forschungszentrum Karlsruhe, 2000.
Tikhonov, A.: On the solution of incorrectly stated problems and method of regularization, Dokl. Akad. Nauk. SSSR, 151, 501–504, 1963.
Twomey, S.: On the Numerical Solution of Fredholm Integral Equations of the First Kind by the Inversion of the Linear System Produced by Quadrature, Journal of the ACM, 10, 97–101, 1963.
von Clarmann, T., Ceccherini, S., Doicu, A., Dudhia, A., Funke, B., Grabowski, U., Hilgers, S., Jay, V., Linden, A., López-Puertas, M., Mart\'\in-Torres, F.-J., Payne, V., Reburn, J., Ridolfi, M., Schreier, F., Schwarz, G., Siddans, R., and Steck, T.: A blind test retrieval experiment for infrared limb emission spectrometry, J. Geophys. Res., 108, 4746, doi:10.1029/2003JD003835, 2003a.
von Clarmann, T., Glatthor, N., Grabowski, U., Höpfner, M., Kellmann, S., Kiefer, M., Linden, A., Mengistu Tsidu, G., Milz, M., Steck, T., Stiller, G P., Wang, D Y., Fischer, H., Funke, B., Gil-López, S., and López-Puertas, M.: Retrieval of temperature and tangent altitude pointing from limb emission spectra recorded from space by the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS), J. Geophys. Res., 108, 4736, doi:10.1029/2003JD003602, 2003b. %
%von Clarmann, T., Glatthor, N., Grabowski, U., Höpfner, M., Kellmann, S., % Linden, A., Mengistu Tsidu, G., Milz, M., Steck, T., Stiller, G P., % Fischer, H., and Funke, B.: Global stratospheric HOCl distributions % retrieved from infrared limb emission spectra recorded by the Michelson % Interferometer for Passive Atmospheric Sounding (MIPAS), % J. Geophys. Res., 111, D05311, doi:10.1029/2005JD005939, 2006.
Wetzel, G., Oelhaf, H., Ruhnke, R., Friedl-Vallon, F., Kleinert, A., Kouker, W., Maucher, G., Reddmann, T., Seefeldner, M., Stowasser, M., Trieschmann, O., von Clarmann, T., and Fischer, H.: NO<sub>y</sub> partitioning and budget and its correlation with N<sub>2</sub>O in the Arctic vortex and in summer midlatitudes in 1997, J. Geophys. Res., 107, 4280, doi:10.1029/2001JD000916, 2002.