Allen, E., Baglama, J., and Boyd, S.: Numerical approximation of the product of
the square root of a matrix with a vector, Linear Algebra and its
Applications, 310, 167–181, https://doi.org/10.1016/s0024-3795(00)00068-9, 2000. a
Bai, Y. and Wang, D.: On the Comparison om Trilinear, Cubic Spline, and Fuzzy
Interpolation Methods in the High-Accuracy Measurements, IEEE T. Fuzzy Syst., 18, 1016–1022, https://doi.org/10.1109/TFUZZ.2010.2064170, 2010. a
Birner, T.: Fine-scale structure of the extratropical tropopause region, J.
Geophys. Res., 111, D04104, https://doi.org/10.1029/2005JD006301, 2006. a, b
Boissonnat, J.-D. and Yvinec, M.: Algorithmic Geometry, Cambridge University
Press, New York, NY, USA, 1998. a
Carlotti, M., Dinelli, B. M., Raspollini, P., and Ridolfi, M.: Geo-fit approach
to the analysis of limb-scanning satellite measurements, Appl. Opt., 40,
1872–1885, https://doi.org/10.1364/AO.40.001872, 2001. a, b
Charney, J. G.: Geostrophic Turbulence, J. Atmos. Sci.,
28, 1087–1095, https://doi.org/10.1175/1520-0469(1971)028<1087:GT>2.0.CO;2, 1971. a
Curtis, A. R.: Discussion of 'A statistical model for water vapour
absorption' by R. M. Goody, Q. J. Roy. Meteor. Soc., 78, 638–640,
1952. a
Delaunay, B.: Sur la sphere vide, B. Acad. Sci. USSR, 7,
793–800, 1934. a
Fehlberg, E.: Some old and new Runge-Kutta formulas with stepsize control and
their error coefficients, Computing, 34, 265–270, https://doi.org/10.1007/BF02253322,
1985. a
FitzGerald, C.: Optimal indexing of the vertices of graphs, Math.
Comput., 28, 825–831, https://doi.org/10.2307/2005704, 1974. a
Forster, P. M. D. F. and Shine, K. P.: Radiative forcing and temperature trends
from stratospheric ozone changes, J. Geophys. Res., 102, 10841–10855,
https://doi.org/10.1029/96JD03510, 1997. a, b
Friedl-Vallon, F., Gulde, T., Hase, F., Kleinert, A., Kulessa, T., Maucher, G., Neubert, T., Olschewski, F., Piesch, C.,
Preusse, P., Rongen, H., Sartorius, C., Schneider, H., Schönfeld, A., Tan, V., Bayer, N., Blank, J., Dapp, R., Ebersoldt, A.,
Fischer, H., Graf, F., Guggenmoser, T., Höpfner, M., Kaufmann, M., Kretschmer, E., Latzko, T., Nordmeyer, H., Oelhaf, H.,
Orphal, J., Riese, M., Schardt, G., Schillings, J., Sha, M. K., Suminska-Ebersoldt, O., and Ungermann, J.: Instrument
concept of the imaging Fourier transform spectrometer GLORIA, Atmos. Meas. Tech., 7, 3565–3577, https://doi.org/10.5194/amt-7-3565-2014, 2014. a, b
Gettelman, A., Hoor, P., Pan, L. L., Randel, W. J., Hegglin, M. I., and Birner,
T.: The extra tropical upper troposphere and lower stratosphere, Rev.
Geophys., 49, RG3003, https://doi.org/10.1029/2011RG000355, 2011. a
Godson, W. L.: The evaluation of infra-red radiative fluxes due to atmospheric
water vapour, Q. J. Roy. Meteor. Soc., 79, 367–379, 1953. a
Golub, G.: Matrix computations, Johns Hopkins University Press, Baltimore,
1996. a
Gordley, L. L. and Russell, J. M.: Rapid inversion of limb radiance data using
an emissivity growth approximation, Appl. Opt., 20, 807–813,
https://doi.org/10.1364/AO.20.000807, 1981. a
Hanke, M.: Conjugate gradient type methods for ill-posed problems, John Wiley
& Sons, 1995. a
Hansen, P. and O'Leary, D.: The Use of the L-Curve in the Regularization of
Discrete Ill-Posed Problems, SIAM J. Sci. Comput., 14,
1487–1503, https://doi.org/10.1137/0914086, 1993. a
Haynes, P. and Anglade, J.: The Vertical-Scale Cascade in Atmospheric Tracers
due to Large-Scale Differential Advection, J. Atmos. Sci., 54, 1121–1136, https://doi.org/10.1175/1520-0469(1997)054<1121:TVSCIA>2.0.CO;2, 1997. a
Hegglin, M. I., Boone, C. D., Manney, G. L., and Walker, K. A.: A global view
of the extratropical tropopause transition layer from Atmospheric Chemistry
Experiment Fourier Transform Spectrometer O3, H2O, and CO, J.
Geophys. Res., 114, D00B11, https://doi.org/10.1029/2008JD009984, 2009. a, b
Hoffmann, L.: Schnelle Spurengasretrieval für das Satellitenexperiment
Envisat MIPAS, vol. 4207 of Berichte des Forschungszentrums
Jülich, Forschungszentrum, Zentralbibliothek, Jülich,
available at: http://juser.fz-juelich.de/record/51782 (last access: 19 December 2018), 2006. a
Hoffmann, L., Kaufmann, M., Spang, R., Müller, R., Remedios, J. J., Moore, D. P., Volk, C. M., von Clarmann, T., and
Riese, M.: Envisat MIPAS measurements of CFC-11: retrieval, validation, and climatology, Atmos. Chem. Phys., 8, 3671–3688,
https://doi.org/10.5194/acp-8-3671-2008, 2008. a
Jülich Supercomputing Centre: JURECA: General-purpose supercomputer at
Jülich Supercomputing Centre, Journal of Large-scale Research
Facilities, 2, A62, https://doi.org/10.17815/jlsrf-2-121,
2016. a
Krisch, I., Preusse, P., Ungermann, J., Dörnbrack, A., Eckermann, S. D., Ern, M., Friedl-Vallon, F., Kaufmann, M., Oelhaf, H., Rapp, M.,
Strube, C., and Riese, M.: First tomographic observations of gravity waves by the infrared limb imager GLORIA, Atmos. Chem. Phys., 17,
14937–14953, https://doi.org/10.5194/acp-17-14937-2017, 2017. a, b
Krisch, I., Ungermann, J., Preusse, P., Kretschmer, E., and Riese, M.: Limited angle tomography of mesoscale
gravity waves by the infrared limb-sounder GLORIA, Atmos. Meas. Tech., 11, 4327–4344, https://doi.org/10.5194/amt-11-4327-2018, 2018. a
Kroese, D. P., Taimre, T., and Botev, Z. I.: Handbook of monte carlo methods,
vol. 706, John Wiley & Sons, 2013. a
Lim, S. and Teo, L.: Generalized Whittle–Matérn random field as a model of
correlated fluctuations, J. Phys. A-Math. Theor.,
42, 105202, https://doi.org/10.1088/1751-8113/42/10/105202, 2009. a, b
Marquardt, D. W.: An Algorithm for Least-Squares Estimation of Nonlinear
Parameters, J. Soc. Ind. Appl. Math.,
11, 431–441, https://doi.org/10.1137/0111030, 1963. a
Preusse, P., Eckermann, S. D., and Ern, M.: Transparency of the atmosphere to
short horizontal wavelength gravity waves, J. Geophys. Res., 113, D24104,
https://doi.org/10.1029/2007JD009682, 2008. a
Riese, M., Ploeger, F., Rap, A., Vogel, B., Konopka, P., Dameris, M., and
Forster, P.: Impact of uncertainties in atmospheric mixing on simulated
UTLS composition and related radiative effects, J. Geophys. Res., 117,
D1605, https://doi.org/10.1029/2012JD017751, 2012. a, b
Riese, M., Oelhaf, H., Preusse, P., Blank, J., Ern, M., Friedl-Vallon, F., Fischer, H., Guggenmoser, T., Höpfner, M., Hoor, P.,
Kaufmann, M., Orphal, J., Plöger, F., Spang, R., Suminska-Ebersoldt, O., Ungermann, J., Vogel, B., and Woiwode, W.: Gimballed Limb
Observer for Radiance Imaging of the Atmosphere (GLORIA) scientific objectives, Atmos. Meas. Tech., 7, 1915–1928, https://doi.org/10.5194/amt-7-1915-2014, 2014. a
Rodgers, C. D.: Inverse Methods for Atmospheric Sounding: Theory and Practice,
vol. 2 of Series on Atmospheric, Oceanic and Planetary Physics, World
Scientific, Singapore, 2000. a, b, c, d, e
Saad, Y.: Iterative Methods for Sparse Linear Systems, Society for Industrial
and Applied Mathematics, second edn., https://doi.org/10.1137/1.9780898718003, 2003. a, b
Skiena, S.: The algorithm design manual, TELOS–the Electronic Library of
Science, Santa Clara, CA, 1998.
a
Sparling, L. C., Wei, J. C., and Avallone, L. M.: Estimating the impact of
small-scale variability in satellite measurement validation, J.
Geophys. Res.-Atmos., 111, D20310, https://doi.org/10.1029/2005JD006943,
2006. a, b
Steck, T., Höpfner, M., von Clarmann, T., and Grabowski, U.: Tomographic
retrieval of atmospheric parameters from infrared limb emission observations,
Appl. Opt., 44, 3291–3301, https://doi.org/10.1364/AO.44.003291, 2005. a, b, c, d
Tarantola, A.: Inverse Problem Theory Methods for Data Fitting and Model
Parameter Estimation, Elsevier Science, 2013. a, b, c
Tikhonov, A. N. and Arsenin, V. Y.: Solutions of ill-posed problems, Winston,
Washington D.C., USA, 1977. a, b
Ungermann, J.: Improving retrieval quality for airborne limb sounders by horizontal regularisation,
Atmos. Meas. Tech., 6, 15–32, https://doi.org/10.5194/amt-6-15-2013, 2013. a, b
Ungermann, J., Kaufmann, M., Hoffmann, L., Preusse, P., Oelhaf, H., Friedl-Vallon, F., and Riese, M.: Towards a 3-D
tomographic retrieval for the air-borne limb-imager GLORIA, Atmos. Meas. Tech., 3, 1647–1665, https://doi.org/10.5194/amt-3-1647-2010, 2010. a, b
Ungermann, J., Blank, J., Lotz, J., Leppkes, K., Hoffmann, L., Guggenmoser, T., Kaufmann, M., Preusse, P., Naumann, U., and
Riese, M.: A 3-D tomographic retrieval approach with advection compensation for the air-borne limb-imager GLORIA,
Atmos. Meas. Tech., 4, 2509–2529, https://doi.org/10.5194/amt-4-2509-2011, 2011. a, b, c, d, e, f
Weinreb, M. P. and Neuendorffer, A. C.: Method to Apply Homogeneous-path
Transmittance Models to Inhomogeneous Atmospheres, J. Atmos. Sci., 30,
662–666, 1973. a
Worden, J. R., Bowman, K. W., and Jones, D. B.: Two-dimensional
characterization of atmospheric profile retrievals from limb sounding
observations, J. Quant. Spectrosc. Ra.,
86, 45–71, 2004. a, b