Comparing Sudden Stratospheric Warming Definitions in Reanalysis Data

© 2015 American Meteorological Society. This study was supported by the Spanish Ministry of Science and Innovation (MCINN) through the MATRES (CGL2012-34221) project and the EU FP7 program through the StratoClim project (603557). We thank W. Seviour and D. Mitchell for providing the onset dates of t...

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Main Authors: Palmeiro Nuñez, Froila María, Barriopedro Cepero, David, García Herrera, Ricardo Francisco, Calvo Fernández, Natalia
Format: Article in Journal/Newspaper
Language:English
Published: American Meteorological Society 2015
Subjects:
52
Climatology
Troposphere
Weather
Astrofísica
Astronomía (Física)
Arctic
Online Access:https://hdl.handle.net/20.500.14352/24220
https://doi.org/10.1175/JCLI-D-15-0004.1
id ftunivcmadrid:oai:docta.ucm.es:20.500.14352/24220
record_format openpolar
institution Open Polar
collection Docta Complutense (Universidad Complutense de Madrid - UCM)
op_collection_id ftunivcmadrid
language English
topic 52
Climatology
Troposphere
Weather
Astrofísica
Astronomía (Física)
spellingShingle 52
Climatology
Troposphere
Weather
Astrofísica
Astronomía (Física)
Palmeiro Nuñez, Froila María
Barriopedro Cepero, David
García Herrera, Ricardo Francisco
Calvo Fernández, Natalia
Comparing Sudden Stratospheric Warming Definitions in Reanalysis Data
topic_facet 52
Climatology
Troposphere
Weather
Astrofísica
Astronomía (Física)
description © 2015 American Meteorological Society. This study was supported by the Spanish Ministry of Science and Innovation (MCINN) through the MATRES (CGL2012-34221) project and the EU FP7 program through the StratoClim project (603557). We thank W. Seviour and D. Mitchell for providing the onset dates of the SSWs detected with their definition in the ERA reanalyses. We thank A. Butler and two anonymous reviewers for their useful comments and recommendations. Sudden stratospheric warmings (SSWs) are characterized by a pronounced increase of the stratospheric polar temperature during the winter season. Different definitions have been used in the literature to diagnose the occurrence of SSWs, yielding discrepancies in the detected events. The aim of this paper is to compare the SSW climatologies obtained by different methods using reanalysis data. The occurrences of Northern Hemisphere SSWs during the extended-winter season and the 1958-2014 period have been identified for a suite of eight representative definitions and three different reanalyses. Overall, and despite the differences in the number and exact dates of occurrence of SSWs, the main climatological signatures of SSWs are not sensitive to the considered reanalysis.The mean frequency of SSWs is 6.7 events decade^-1, but it ranges from 4 to 10 events, depending on the method. The seasonal cycle of events is statistically indistinguishable across definitions, with a common peak in January. However, the multidecadal variability is method dependent, with only two definitions displaying minimum frequencies in the 1990s. An analysis of the mean signatures of SSWs in the stratosphere revealed negligible differences among methods compared to the large case-to-case variability within a given definition.The stronger and more coherent tropospheric signals before and after SSWs are associated with major events, which are detected by most methods. The tropospheric signals of minor SSWs are less robust, representing the largest source of discrepancy across definitions. ...
format Article in Journal/Newspaper
author Palmeiro Nuñez, Froila María
Barriopedro Cepero, David
García Herrera, Ricardo Francisco
Calvo Fernández, Natalia
author_facet Palmeiro Nuñez, Froila María
Barriopedro Cepero, David
García Herrera, Ricardo Francisco
Calvo Fernández, Natalia
author_sort Palmeiro Nuñez, Froila María
title Comparing Sudden Stratospheric Warming Definitions in Reanalysis Data
title_short Comparing Sudden Stratospheric Warming Definitions in Reanalysis Data
title_full Comparing Sudden Stratospheric Warming Definitions in Reanalysis Data
title_fullStr Comparing Sudden Stratospheric Warming Definitions in Reanalysis Data
title_full_unstemmed Comparing Sudden Stratospheric Warming Definitions in Reanalysis Data
title_sort comparing sudden stratospheric warming definitions in reanalysis data
publisher American Meteorological Society
publishDate 2015
url https://hdl.handle.net/20.500.14352/24220
https://doi.org/10.1175/JCLI-D-15-0004.1
genre Arctic
genre_facet Arctic
op_relation StratoClim (603557)
MATRES (CGL2012-34221)
Andrews, D. G., J. R. Holton, and C. B. Leovy, 1987: Middle Atmosphere Dynamics. International Geophysics Series, Vol. 40, Academic Press, 489 pp. Baldwin, M. P., and T. J. Dunkerton, 2001: Stratospheric harbingers of anomalous weather regimes. Science, 294, 581–584, doi:10.1126/science.1063315. ——, and D. W. J. Thompson, 2009: A critical comparison of stratosphere–troposphere coupling indices. Quart. J. Roy. Meteor. Soc., 135, 1661–1672, doi:10.1002/qj.479. Bancalá, S., K. Krüger, and M. Giorgetta, 2012: The preconditioning of major sudden stratospheric warmings. J. Geophys. Res., 117, D04101, doi:10.1029/2011JD016769. Barriopedro, D., and N. Calvo, 2014: On the relationship between ENSO, stratospheric sudden warmings, and blocking. J. Climate, 27, 4704–4720, doi:10.1175/JCLI-D-13-00770.1. Blume, C., K. Matthes, and I. Horenko, 2012: Supervised learning approaches to classify sudden stratospheric warming events. J. Atmos., 69, 1824–1840, doi:10.1175/JAS-D110194.1. Butler, A. H., E. P. Gerber, D. Mitchell, and W. Seviour, 2014: New efforts in developing a standard definition for sudden stratospheric warmings. SPARC Newsletter, No. 43, SPARC Office, Toronto, ON, Canada, 23–24. ——, D. J. Seidel, S. C. Hardiman, N. Butchart, T. Birner, and A. Match, 2015: Defining sudden stratospheric warmings. Bull. Amer. Meteor. Soc., doi:10.1175/BAMS-D-13-00173.1, in press. Charlton, A. J., and L. M. Polvani, 2007: A new look at stratospheric sudden warmings. Part I: Climatology and modeling benchmarks. J. Climate, 20, 449–469, doi:10.1175/JCLI3996.1. Cohen, J., and J. Jones, 2011: Tropospheric precursors and stratospheric warmings. J. Climate, 24, 6562–6572, doi:10.1175/2011JCLI4160.1. Dee, D. P., and Coauthors, 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553–597, doi:10.1002/qj.828. de la Torre, L., R. R. García, D. Barriopedro, and A. Chandran, 2012: Climatology and characteristics of stratospheric sudden warmings in the Whole Atmosphere Community Climate Model. J. Geophys. Res., 117, D04110, doi:10.1029/2011JD016840. Ebita, A., and Coauthors, 2011: The Japanese 55-year Reanalysis ‘‘JRA-55’’: An interim report. SOLA, 7, 149–152, doi:10.2151/sola.2011-038. Gómez Escolar, M., S. Fueglistaler, N. Calvo, and D. Barriopedro, 2012: Changes in polar stratospheric temperature climatology in relation to stratospheric sudden warming occurrence. Geophys. Res. Lett., 39, L22802, doi:10.1029/2012GL053632. Hannachi, A., D. Mitchell, L. Gray, and A. Charlton Pérez, 2011: On the use of geometric moments to examine the continuum of sudden stratospheric warmings. J. Atmos. Sci., 68, 657–674, doi:10.1175/2010JAS3585.1. Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77, 437–471, doi:10.1175/1520-0477(1996)077,0437:TNYRP.2.0.CO;2. Kodera, K., 2006: Influence of stratospheric sudden warming on the equatorial troposphere. Geophys. Res. Lett., 33, L06804, doi:10.1029/2005GL024510. ——, Y. Kuroda, and S. Pawson, 2000: Stratospheric sudden warmings and slowly propagating zonal-mean zonal wind anomalies. J. Geophys. Res., 105, 12 351–12 359, doi:10.1029/2000JD900095. Labitzke, K., 1981: Stratospheric-mesospheric midwinter disturbances: A summary of observed characteristics. J. Geophys. Res., 86, 9665–9678, doi:10.1029/JC086iC10p09665. ——, and B. Naujokat, 2000: The lower Arctic stratosphere in winter since 1952. SPARC Newsletter, No. 15, SPARC Office, Toronto, ON, Canada, 11–14. Limpasuvan, V., D. W. J. Thompson, and D. L. Hartmann, 2004: The life cycle of the Northern Hemisphere sudden stratospheric warmings. J. Climate, 17, 2584–2596, doi:10.1175/1520-0442(2004)017,2584:TLCOTN.2.0.CO;2. Martineau, P., and S.-W. Son, 2010: Quality of reanalysis data during stratospheric vortex weakening and intensification events. Geophys. Res. Lett., 37, L22801, doi:10.1029/2010GL045237. ——, and ——, 2013: Planetary-scale wave activity as a source of varying tropospheric response to stratospheric sudden warming events: A case study. J. Geophys. Res. Atmos., 118, 10 994–11 006, doi:10.1002/jgrd.50871. Matsuno, T., 1971: A dynamical model of the stratospheric sudden warming. J. Atmos. Sci., 28, 1479–1494, doi:10.1175/ 1520-0469(1971)028,1479:ADMOTS.2.0.CO;2. Matthewman, N. J., J. G. Esler, A. J. Charlton Pérez, and L. M. Polvani, 2009: A new look at stratospheric sudden warmings. Part III: Polar vortex evolution and vertical structure. J. Climate, 22, 1566–1585, doi:10.1175/2008JCLI2365.1. McInturff, R. M., 1978: Stratospheric warmings: Synoptic, dynamic and general-circulation aspects. NASA Ref. Publ. 1017, 19 pp. Mitchell, D. M., A. J. Charlton Pérez, and L. J. Gray, 2011: Characterizing the variability and extremes of the stratospheric polar vortices using 2D moment analysis. J. Atmos. Sci., 68, 1194–1213, doi:10.1175/2010JAS3555.1. Nakagawa, K. I., and K. Yamazaki, 2006: What kind of stratospheric sudden warming propagates to the troposphere? Geophys. Res. Lett., 33, L04801, doi:10.1029/2005GL024784. Naujokat, B., and S. Pawson, 1996: The cold stratospheric winters 1994/1995 and 1995/1996. Geophys. Res. Lett., 23, 3703–3706, doi:10.1029/96GL03614. Scherhag, R., 1952: Die explosionsartige Stratosphadrenerwarmungen des Spadtwinters, 1951–1952. Ber. Dtsch. Wetterdienst, 38, 51–63. Seviour, W., D. M. Mitchell, and L. J. Gray, 2013: A practical method to identify displaced and split stratospheric polar vortex events. Geophys. Res. Lett., 40, 5268–5273, doi:10.1002/grl.50927. Sigmond, M., J. F. Scinocca, V. V. Kharin, and T. G. Shepherd, 2013: Enhanced seasonal forecast skill following stratospheric sudden warmings. Nat. Geosci., 6, 98–102, doi:10.1038/ngeo1698. Taguchi, M., and D. L. Hartmann, 2005: Interference of extratropical surface climate anomalies induced by El Niño and stratospheric sudden warmings. Geophys. Res. Lett., 32, L04709, doi:10.1029/2004GL022004. Thompson, D. W. J., M. P. Baldwin, and J. M. Wallace, 2002: Stratospheric connection to Northern Hemisphere wintertime weather: Implications for prediction. J. Climate, 15, 1421–1428, doi:10.1175/1520-0442(2002)015,1421: SCTNHW.2.0.CO;2. Tripathi, O. P., and Coauthors, 2015: The predictability of the extratropical stratosphere on monthly time-scales and its impact on the skill of tropospheric forecasts. Quart. J. Roy. Meteor. Soc., 141, 987–1003, doi:10.1002/qj.2432. Uppala, S. M., and Coauthors, 2005: The ERA-40 Re-Analysis. Quart. J. Roy. Meteor. Soc., 131, 2961–3012, doi:10.1256/qj.04.176. Waugh, D. W., and W. J. Randel, 1999: Climatology of Arctic and Antarctic polar vortices using elliptical diagnostics. J. Atmos. Sci., 56, 1594–1613, doi:10.1175/1520-0469(1999)056,1594:COAAAP.2.0.CO;2. Wilks, D. S., 2011: Statistical Methods in the Atmospheric Sciences. 3rd ed. International Geophysics Series, Vol. 100, Academic Press, 676 pp. WMO/IQSY, 1964: International Years of the Quiet Sun (IQSY) 1964–1965: Alert messages with special references to stratwarms. WMO/IQSY Rep. 6, Secretariat of the World Meteorological Organization, 258 pp. Yoden, S., T. Yamaga, S. Pawson, and U. Langematz, 1999: A composite analysis of the stratospheric sudden warmings simulated in a perpetual January integration of the Berlin TSM GCM. J. Meteor. Soc. Japan, 77, 431–445.
https://hdl.handle.net/20.500.14352/24220
0894-8755
doi:10.1175/JCLI-D-15-0004.1
op_rights open access
op_doi https://doi.org/20.500.14352/2422010.1175/JCLI-D-15-0004.110.1126/science.1063315
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spelling ftunivcmadrid:oai:docta.ucm.es:20.500.14352/24220 2024-09-15T17:52:03+00:00 Comparing Sudden Stratospheric Warming Definitions in Reanalysis Data Palmeiro Nuñez, Froila María Barriopedro Cepero, David García Herrera, Ricardo Francisco Calvo Fernández, Natalia 2015-09 application/pdf https://hdl.handle.net/20.500.14352/24220 https://doi.org/10.1175/JCLI-D-15-0004.1 eng eng American Meteorological Society StratoClim (603557) MATRES (CGL2012-34221) Andrews, D. G., J. R. Holton, and C. B. Leovy, 1987: Middle Atmosphere Dynamics. International Geophysics Series, Vol. 40, Academic Press, 489 pp. Baldwin, M. P., and T. J. Dunkerton, 2001: Stratospheric harbingers of anomalous weather regimes. Science, 294, 581–584, doi:10.1126/science.1063315. ——, and D. W. J. Thompson, 2009: A critical comparison of stratosphere–troposphere coupling indices. Quart. J. Roy. Meteor. Soc., 135, 1661–1672, doi:10.1002/qj.479. Bancalá, S., K. Krüger, and M. Giorgetta, 2012: The preconditioning of major sudden stratospheric warmings. J. Geophys. Res., 117, D04101, doi:10.1029/2011JD016769. Barriopedro, D., and N. Calvo, 2014: On the relationship between ENSO, stratospheric sudden warmings, and blocking. J. Climate, 27, 4704–4720, doi:10.1175/JCLI-D-13-00770.1. Blume, C., K. Matthes, and I. Horenko, 2012: Supervised learning approaches to classify sudden stratospheric warming events. J. Atmos., 69, 1824–1840, doi:10.1175/JAS-D110194.1. Butler, A. H., E. P. Gerber, D. Mitchell, and W. Seviour, 2014: New efforts in developing a standard definition for sudden stratospheric warmings. SPARC Newsletter, No. 43, SPARC Office, Toronto, ON, Canada, 23–24. ——, D. J. Seidel, S. C. Hardiman, N. Butchart, T. Birner, and A. Match, 2015: Defining sudden stratospheric warmings. Bull. Amer. Meteor. Soc., doi:10.1175/BAMS-D-13-00173.1, in press. Charlton, A. J., and L. M. Polvani, 2007: A new look at stratospheric sudden warmings. Part I: Climatology and modeling benchmarks. J. Climate, 20, 449–469, doi:10.1175/JCLI3996.1. Cohen, J., and J. Jones, 2011: Tropospheric precursors and stratospheric warmings. J. Climate, 24, 6562–6572, doi:10.1175/2011JCLI4160.1. Dee, D. P., and Coauthors, 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553–597, doi:10.1002/qj.828. de la Torre, L., R. R. García, D. Barriopedro, and A. Chandran, 2012: Climatology and characteristics of stratospheric sudden warmings in the Whole Atmosphere Community Climate Model. J. Geophys. Res., 117, D04110, doi:10.1029/2011JD016840. Ebita, A., and Coauthors, 2011: The Japanese 55-year Reanalysis ‘‘JRA-55’’: An interim report. SOLA, 7, 149–152, doi:10.2151/sola.2011-038. Gómez Escolar, M., S. Fueglistaler, N. Calvo, and D. Barriopedro, 2012: Changes in polar stratospheric temperature climatology in relation to stratospheric sudden warming occurrence. Geophys. Res. Lett., 39, L22802, doi:10.1029/2012GL053632. Hannachi, A., D. Mitchell, L. Gray, and A. Charlton Pérez, 2011: On the use of geometric moments to examine the continuum of sudden stratospheric warmings. J. Atmos. Sci., 68, 657–674, doi:10.1175/2010JAS3585.1. Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77, 437–471, doi:10.1175/1520-0477(1996)077,0437:TNYRP.2.0.CO;2. Kodera, K., 2006: Influence of stratospheric sudden warming on the equatorial troposphere. Geophys. Res. Lett., 33, L06804, doi:10.1029/2005GL024510. ——, Y. Kuroda, and S. Pawson, 2000: Stratospheric sudden warmings and slowly propagating zonal-mean zonal wind anomalies. J. Geophys. Res., 105, 12 351–12 359, doi:10.1029/2000JD900095. Labitzke, K., 1981: Stratospheric-mesospheric midwinter disturbances: A summary of observed characteristics. J. Geophys. Res., 86, 9665–9678, doi:10.1029/JC086iC10p09665. ——, and B. Naujokat, 2000: The lower Arctic stratosphere in winter since 1952. SPARC Newsletter, No. 15, SPARC Office, Toronto, ON, Canada, 11–14. Limpasuvan, V., D. W. J. Thompson, and D. L. Hartmann, 2004: The life cycle of the Northern Hemisphere sudden stratospheric warmings. J. Climate, 17, 2584–2596, doi:10.1175/1520-0442(2004)017,2584:TLCOTN.2.0.CO;2. Martineau, P., and S.-W. Son, 2010: Quality of reanalysis data during stratospheric vortex weakening and intensification events. Geophys. Res. Lett., 37, L22801, doi:10.1029/2010GL045237. ——, and ——, 2013: Planetary-scale wave activity as a source of varying tropospheric response to stratospheric sudden warming events: A case study. J. Geophys. Res. Atmos., 118, 10 994–11 006, doi:10.1002/jgrd.50871. Matsuno, T., 1971: A dynamical model of the stratospheric sudden warming. J. Atmos. Sci., 28, 1479–1494, doi:10.1175/ 1520-0469(1971)028,1479:ADMOTS.2.0.CO;2. Matthewman, N. J., J. G. Esler, A. J. Charlton Pérez, and L. M. Polvani, 2009: A new look at stratospheric sudden warmings. Part III: Polar vortex evolution and vertical structure. J. Climate, 22, 1566–1585, doi:10.1175/2008JCLI2365.1. McInturff, R. M., 1978: Stratospheric warmings: Synoptic, dynamic and general-circulation aspects. NASA Ref. Publ. 1017, 19 pp. Mitchell, D. M., A. J. Charlton Pérez, and L. J. Gray, 2011: Characterizing the variability and extremes of the stratospheric polar vortices using 2D moment analysis. J. Atmos. Sci., 68, 1194–1213, doi:10.1175/2010JAS3555.1. Nakagawa, K. I., and K. Yamazaki, 2006: What kind of stratospheric sudden warming propagates to the troposphere? Geophys. Res. Lett., 33, L04801, doi:10.1029/2005GL024784. Naujokat, B., and S. Pawson, 1996: The cold stratospheric winters 1994/1995 and 1995/1996. Geophys. Res. Lett., 23, 3703–3706, doi:10.1029/96GL03614. Scherhag, R., 1952: Die explosionsartige Stratosphadrenerwarmungen des Spadtwinters, 1951–1952. Ber. Dtsch. Wetterdienst, 38, 51–63. Seviour, W., D. M. Mitchell, and L. J. Gray, 2013: A practical method to identify displaced and split stratospheric polar vortex events. Geophys. Res. Lett., 40, 5268–5273, doi:10.1002/grl.50927. Sigmond, M., J. F. Scinocca, V. V. Kharin, and T. G. Shepherd, 2013: Enhanced seasonal forecast skill following stratospheric sudden warmings. Nat. Geosci., 6, 98–102, doi:10.1038/ngeo1698. Taguchi, M., and D. L. Hartmann, 2005: Interference of extratropical surface climate anomalies induced by El Niño and stratospheric sudden warmings. Geophys. Res. Lett., 32, L04709, doi:10.1029/2004GL022004. Thompson, D. W. J., M. P. Baldwin, and J. M. Wallace, 2002: Stratospheric connection to Northern Hemisphere wintertime weather: Implications for prediction. J. Climate, 15, 1421–1428, doi:10.1175/1520-0442(2002)015,1421: SCTNHW.2.0.CO;2. Tripathi, O. P., and Coauthors, 2015: The predictability of the extratropical stratosphere on monthly time-scales and its impact on the skill of tropospheric forecasts. Quart. J. Roy. Meteor. Soc., 141, 987–1003, doi:10.1002/qj.2432. Uppala, S. M., and Coauthors, 2005: The ERA-40 Re-Analysis. Quart. J. Roy. Meteor. Soc., 131, 2961–3012, doi:10.1256/qj.04.176. Waugh, D. W., and W. J. Randel, 1999: Climatology of Arctic and Antarctic polar vortices using elliptical diagnostics. J. Atmos. Sci., 56, 1594–1613, doi:10.1175/1520-0469(1999)056,1594:COAAAP.2.0.CO;2. Wilks, D. S., 2011: Statistical Methods in the Atmospheric Sciences. 3rd ed. International Geophysics Series, Vol. 100, Academic Press, 676 pp. WMO/IQSY, 1964: International Years of the Quiet Sun (IQSY) 1964–1965: Alert messages with special references to stratwarms. WMO/IQSY Rep. 6, Secretariat of the World Meteorological Organization, 258 pp. Yoden, S., T. Yamaga, S. Pawson, and U. Langematz, 1999: A composite analysis of the stratospheric sudden warmings simulated in a perpetual January integration of the Berlin TSM GCM. J. Meteor. Soc. Japan, 77, 431–445. https://hdl.handle.net/20.500.14352/24220 0894-8755 doi:10.1175/JCLI-D-15-0004.1 open access 52 Climatology Troposphere Weather Astrofísica Astronomía (Física) journal article 2015 ftunivcmadrid https://doi.org/20.500.14352/2422010.1175/JCLI-D-15-0004.110.1126/science.1063315 2024-08-29T23:43:41Z © 2015 American Meteorological Society. This study was supported by the Spanish Ministry of Science and Innovation (MCINN) through the MATRES (CGL2012-34221) project and the EU FP7 program through the StratoClim project (603557). We thank W. Seviour and D. Mitchell for providing the onset dates of the SSWs detected with their definition in the ERA reanalyses. We thank A. Butler and two anonymous reviewers for their useful comments and recommendations. Sudden stratospheric warmings (SSWs) are characterized by a pronounced increase of the stratospheric polar temperature during the winter season. Different definitions have been used in the literature to diagnose the occurrence of SSWs, yielding discrepancies in the detected events. The aim of this paper is to compare the SSW climatologies obtained by different methods using reanalysis data. The occurrences of Northern Hemisphere SSWs during the extended-winter season and the 1958-2014 period have been identified for a suite of eight representative definitions and three different reanalyses. Overall, and despite the differences in the number and exact dates of occurrence of SSWs, the main climatological signatures of SSWs are not sensitive to the considered reanalysis.The mean frequency of SSWs is 6.7 events decade^-1, but it ranges from 4 to 10 events, depending on the method. The seasonal cycle of events is statistically indistinguishable across definitions, with a common peak in January. However, the multidecadal variability is method dependent, with only two definitions displaying minimum frequencies in the 1990s. An analysis of the mean signatures of SSWs in the stratosphere revealed negligible differences among methods compared to the large case-to-case variability within a given definition.The stronger and more coherent tropospheric signals before and after SSWs are associated with major events, which are detected by most methods. The tropospheric signals of minor SSWs are less robust, representing the largest source of discrepancy across definitions. ... Article in Journal/Newspaper Arctic Docta Complutense (Universidad Complutense de Madrid - UCM)

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