Articles | Volume 14, issue 4
https://doi.org/10.5194/amt-14-2993-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Special issue:
https://doi.org/10.5194/amt-14-2993-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
A method for random uncertainties validation and probing the natural variability with application to TROPOMI on board Sentinel-5P total ozone measurements
Viktoria F. Sofieva
CORRESPONDING AUTHOR
Space and Earth Observation Centre, Finnish Meteorological Institute, Helsinki, Finland
Hei Shing Lee
Space and Earth Observation Centre, Finnish Meteorological Institute, Helsinki, Finland
Atmospheric Sciences Department, University of Helsinki, Helsinki, Finland
Johanna Tamminen
Space and Earth Observation Centre, Finnish Meteorological Institute, Helsinki, Finland
Christophe Lerot
Belgian Institute for Space Aeronomy (BIRA-IASB), Brussels, Belgium
Fabian Romahn
German Aerospace Centre (DLR), Remote Sensing Technology Institute,
Oberpfaffenhofen, Germany
Diego G. Loyola
German Aerospace Centre (DLR), Remote Sensing Technology Institute,
Oberpfaffenhofen, Germany
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Tropospheric ozone affects air quality and climate, being a pollutant and a greenhouse gas. We analyze satellite data of tropospheric ozone columns obtained by combining two types of observations: one providing stratospheric and the other total ozone. We compare common climatological features and study the influence of the tropopause (troposphere to stratosphere boundary) on the results. We also examine trends over the last 20 years and compare satellite data with ozonesondes to identify drifts.
Arno Keppens, Daan Hubert, José Granville, Oindrila Nath, Jean-Christopher Lambert, Catherine Wespes, Pierre-François Coheur, Cathy Clerbaux, Anne Boynard, Richard Siddans, Barry Latter, Brian Kerridge, Serena Di Pede, Pepijn Veefkind, Juan Cuesta, Gaelle Dufour, Klaus-Peter Heue, Melanie Coldewey-Egbers, Diego Loyola, Andrea Orfanoz-Cheuquelaf, Swathi Maratt Satheesan, Kai-Uwe Eichmann, Alexei Rozanov, Viktoria F. Sofieva, Jerald R. Ziemke, Antje Inness, Roeland Van Malderen, and Lars Hoffmann
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The first Tropospheric Ozone Assessment Report (TOAR) encountered discrepancies between several satellite sensors’ estimates of the distribution and change of ozone in the free troposphere. Therefore, contributing to the second TOAR, we harmonise as much as possible the observational perspective of sixteen tropospheric ozone products from satellites. This only partially accounts for the observed discrepancies, with a reduction of 10–40 % of the inter-product dispersion upon harmonisation.
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Earth Syst. Sci. Data, 16, 5227–5241, https://doi.org/10.5194/essd-16-5227-2024, https://doi.org/10.5194/essd-16-5227-2024, 2024
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Climate-related studies need information about the distribution of stratospheric aerosols, which influence the energy balance of the Earth’s atmosphere. In this work, we present a merged dataset of vertically resolved stratospheric aerosol extinction coefficients, which is derived from data of six limb and occultation satellite instruments. The created aerosol climate record covers the period from October 1984 to December 2023. It can be used in various climate-related studies.
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Atmos. Meas. Tech., 17, 3669–3678, https://doi.org/10.5194/amt-17-3669-2024, https://doi.org/10.5194/amt-17-3669-2024, 2024
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Atmos. Meas. Tech., 17, 3085–3101, https://doi.org/10.5194/amt-17-3085-2024, https://doi.org/10.5194/amt-17-3085-2024, 2024
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We have developed the new multi-wavelength dataset of aerosol extinction profiles, which are retrieved from the averaged transmittance spectra by the Global Ozone Monitoring by Occultation of Stars instrument aboard Envisat. The retrieved aerosol extinction profiles are provided in the altitude range 10–40 km at 400, 440, 452, 470, 500, 525, 550, 672 and 750 nm for the period 2002–2012. FMI-GOMOSaero aerosol profiles have improved quality; they are in good agreement with other datasets.
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Atmos. Meas. Tech., 16, 1881–1899, https://doi.org/10.5194/amt-16-1881-2023, https://doi.org/10.5194/amt-16-1881-2023, 2023
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The paper presents the updated SAGE-CCI-OMPS+ climate data record of monthly zonal mean ozone profiles. This dataset covers the stratosphere and combines measurements by nine limb and occultation satellite instruments (SAGE II, OSIRIS, MIPAS, SCIAMACHY, GOMOS, ACE-FTS, OMPS-LP, POAM III, and SAGE III/ISS). The update includes new versions of MIPAS, ACE-FTS, and OSIRIS datasets and introduces data from additional sensors (POAM III and SAGE III/ISS) and retrieval processors (OMPS-LP).
Sophie Godin-Beekmann, Niramson Azouz, Viktoria F. Sofieva, Daan Hubert, Irina Petropavlovskikh, Peter Effertz, Gérard Ancellet, Doug A. Degenstein, Daniel Zawada, Lucien Froidevaux, Stacey Frith, Jeannette Wild, Sean Davis, Wolfgang Steinbrecht, Thierry Leblanc, Richard Querel, Kleareti Tourpali, Robert Damadeo, Eliane Maillard Barras, René Stübi, Corinne Vigouroux, Carlo Arosio, Gerald Nedoluha, Ian Boyd, Roeland Van Malderen, Emmanuel Mahieu, Dan Smale, and Ralf Sussmann
Atmos. Chem. Phys., 22, 11657–11673, https://doi.org/10.5194/acp-22-11657-2022, https://doi.org/10.5194/acp-22-11657-2022, 2022
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An updated evaluation up to 2020 of stratospheric ozone profile long-term trends at extrapolar latitudes based on satellite and ground-based records is presented. Ozone increase in the upper stratosphere is confirmed, with significant trends at most latitudes. In this altitude region, a very good agreement is found with trends derived from chemistry–climate model simulations. Observed and modelled trends diverge in the lower stratosphere, but the differences are non-significant.
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Atmos. Meas. Tech., 15, 5129–5140, https://doi.org/10.5194/amt-15-5129-2022, https://doi.org/10.5194/amt-15-5129-2022, 2022
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Viktoria F. Sofieva, Risto Hänninen, Mikhail Sofiev, Monika Szeląg, Hei Shing Lee, Johanna Tamminen, and Christian Retscher
Atmos. Meas. Tech., 15, 3193–3212, https://doi.org/10.5194/amt-15-3193-2022, https://doi.org/10.5194/amt-15-3193-2022, 2022
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We present tropospheric ozone column datasets that have been created using combinations of total ozone column from OMI and TROPOMI with stratospheric ozone column datasets from several available limb-viewing instruments (MLS, OSIRIS, MIPAS, SCIAMACHY, OMPS-LP, GOMOS). The main results are (i) several methodological developments, (ii) new tropospheric ozone column datasets from OMI and TROPOMI, and (iii) a new high-resolution dataset of ozone profiles from limb satellite instruments.
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This preprint is open for discussion and under review for Atmospheric Measurement Techniques (AMT).
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Carlo Arosio, Viktoria Sofieva, Andrea Orfanoz-Cheuquelaf, Alexei Rozanov, Klaus-Peter Heue, Diego Loyola, Edward Malina, Ryan M. Stauffer, David Tarasick, Roeland Van Malderen, Jerry R. Ziemke, and Mark Weber
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Tropospheric ozone affects air quality and climate, being a pollutant and a greenhouse gas. We analyze satellite data of tropospheric ozone columns obtained by combining two types of observations: one providing stratospheric and the other total ozone. We compare common climatological features and study the influence of the tropopause (troposphere to stratosphere boundary) on the results. We also examine trends over the last 20 years and compare satellite data with ozonesondes to identify drifts.
África Barreto, Francisco Quirós, Omaira E. García, Jorge Pereda-de-Pablo, Daniel González-Fernández, Andrés Bedoya-Velásquez, Michael Sicard, Carmen Córdoba-Jabonero, Marco Iarlori, Vincenzo Rizi, Nickolay Krotkov, Simon Carn, Reijo Roininen, Antonio J. Molina-Arias, A. Fernando Almansa, Óscar Álvarez-Losada, Carla Aramo, Juan José Bustos, Romain Ceolato, Adolfo Comerón, Alicia Felpeto, Rosa D. García, Pablo González-Sicilia, Yenny González, Pascal Hedelt, Miguel Hernández, María-Ángeles López-Cayuela, Diego Loyola, Stavros Meletlidis, Constantino Muñoz-Porcar, Ermanno Pietropaolo, Ramón Ramos, Alejandro Rodríguez-Gómez, Roberto Román, Pedro M. Romero-Campos, Martin Stuefer, Carlos Toledano, and Elsworth Welton
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This preprint is open for discussion and under review for Atmospheric Measurement Techniques (AMT).
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Atmos. Meas. Tech. Discuss., https://doi.org/10.5194/amt-2024-196, https://doi.org/10.5194/amt-2024-196, 2025
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The GOME-type Ozone Profile Essential Climate Variable (GOP-ECV) data record provides monthly mean ozone profiles with global coverage from 1995 to 2021 at a spatial resolution of 5°x5°. Measurements from five nadir-viewing satellite sensors are first harmonized and then merged into a coherent record. The long-term stability of the data record is further improved through scaling of the profiles using as a reference the GOME-type Total Ozone Essential Climate Variable (GTO-ECV) data record.
Arno Keppens, Daan Hubert, José Granville, Oindrila Nath, Jean-Christopher Lambert, Catherine Wespes, Pierre-François Coheur, Cathy Clerbaux, Anne Boynard, Richard Siddans, Barry Latter, Brian Kerridge, Serena Di Pede, Pepijn Veefkind, Juan Cuesta, Gaelle Dufour, Klaus-Peter Heue, Melanie Coldewey-Egbers, Diego Loyola, Andrea Orfanoz-Cheuquelaf, Swathi Maratt Satheesan, Kai-Uwe Eichmann, Alexei Rozanov, Viktoria F. Sofieva, Jerald R. Ziemke, Antje Inness, Roeland Van Malderen, and Lars Hoffmann
EGUsphere, https://doi.org/10.5194/egusphere-2024-3746, https://doi.org/10.5194/egusphere-2024-3746, 2025
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The first Tropospheric Ozone Assessment Report (TOAR) encountered discrepancies between several satellite sensors’ estimates of the distribution and change of ozone in the free troposphere. Therefore, contributing to the second TOAR, we harmonise as much as possible the observational perspective of sixteen tropospheric ozone products from satellites. This only partially accounts for the observed discrepancies, with a reduction of 10–40 % of the inter-product dispersion upon harmonisation.
Ella Kivimäki, Tuula Aalto, Michael Buchwitz, Kari Luojus, Jouni Pulliainen, Kimmo Rautiainen, Oliver Schneising, Anu-Maija Sundström, Johanna Tamminen, Aki Tsuruta, and Hannakaisa Lindqvist
EGUsphere, https://doi.org/10.5194/egusphere-2025-249, https://doi.org/10.5194/egusphere-2025-249, 2025
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We investigate how environmental variables influencing natural methane fluxes explain the large-scale seasonal variability of satellite-observed methane at Northern high latitudes. Our findings show that soil moisture, snow cover, and soil temperature have the strongest influence, with snowmelt playing a surprisingly significant role, likely through soil isolation and wetting. This study highlights the value of multi-satellite observations for understanding large-scale wetland emissions.
Pascal Hedelt, Jens Reichardt, Felix Lauermann, Benjamin Weiß, Nicolas Theys, Alberto Redondas, Africa Barreto, Omaira Garcia, and Diego Loyola
Atmos. Chem. Phys., 25, 1253–1272, https://doi.org/10.5194/acp-25-1253-2025, https://doi.org/10.5194/acp-25-1253-2025, 2025
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The 2021 volcanic eruption of Tajogaite on La Palma is investigated using ground-based and satellite measurements. In addition, the atmospheric transport of the volcanic cloud towards Europe is studied in detail. The amount of SO2 released during the eruption and the height of the volcanic plume are in excellent agreement among the different measurements. Furthermore, volcanic aerosol microphysical properties could be retrieved using a new retrieval approach based on lidar measurements.
Diego Santaren, Janne Hakkarainen, Gerrit Kuhlmann, Erik Koene, Frédéric Chevallier, Iolanda Ialongo, Hannakaisa Lindqvist, Janne Nurmela, Johanna Tamminen, Laia Amorós, Dominik Brunner, and Grégoire Broquet
Atmos. Meas. Tech., 18, 211–239, https://doi.org/10.5194/amt-18-211-2025, https://doi.org/10.5194/amt-18-211-2025, 2025
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This study evaluates data-driven inversion methods for estimating CO2 emissions from local sources, such as power plants and cities, using meteorological data and XCO2 and NO2 satellite images rather than atmospheric transport modeling. We assess and compare the performance of five different methods using simulations of 1 year of satellite images, taken from the upcoming Copernicus CO2 Monitoring Mission, covering 15 power plants and the city of Berlin, Germany.
Viktoria F. Sofieva, Alexei Rozanov, Monika Szelag, John P. Burrows, Christian Retscher, Robert Damadeo, Doug Degenstein, Landon A. Rieger, and Adam Bourassa
Earth Syst. Sci. Data, 16, 5227–5241, https://doi.org/10.5194/essd-16-5227-2024, https://doi.org/10.5194/essd-16-5227-2024, 2024
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Climate-related studies need information about the distribution of stratospheric aerosols, which influence the energy balance of the Earth’s atmosphere. In this work, we present a merged dataset of vertically resolved stratospheric aerosol extinction coefficients, which is derived from data of six limb and occultation satellite instruments. The created aerosol climate record covers the period from October 1984 to December 2023. It can be used in various climate-related studies.
Athina Argyrouli, Diego Loyola, Fabian Romahn, Ronny Lutz, Víctor Molina García, Pascal Hedelt, Klaus-Peter Heue, and Richard Siddans
Atmos. Meas. Tech., 17, 6345–6367, https://doi.org/10.5194/amt-17-6345-2024, https://doi.org/10.5194/amt-17-6345-2024, 2024
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This paper describes a new treatment of the spatial misregistration of cloud properties for Sentinel-5 Precursor, when the footprints of different spectral bands are not perfectly aligned. The methodology exploits synergies between spectrometers and imagers, like TROPOMI and VIIRS. The largest improvements have been identified for heterogeneous scenes at cloud edges. This approach is generic and can also be applied to future Sentinel-4 and Sentinel-5 instruments.
Sora Seo, Pieter Valks, Ronny Lutz, Klaus-Peter Heue, Pascal Hedelt, Víctor Molina García, Diego Loyola, Hanlim Lee, and Jhoon Kim
Atmos. Meas. Tech., 17, 6163–6191, https://doi.org/10.5194/amt-17-6163-2024, https://doi.org/10.5194/amt-17-6163-2024, 2024
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In this study, we developed an advanced retrieval algorithm for tropospheric NO2 columns from geostationary satellite spectrometers and applied it to GEMS measurements. The DLR GEMS NO2 retrieval algorithm follows the heritage from previous and existing algorithms, but improved approaches are applied to reflect the specific features of geostationary satellites. The DLR GEMS NO2 retrievals demonstrate a good capability for monitoring diurnal variability with a high spatial resolution.
Tim Trent, Marc Schröder, Shu-Peng Ho, Steffen Beirle, Ralf Bennartz, Eva Borbas, Christian Borger, Helene Brogniez, Xavier Calbet, Elisa Castelli, Gilbert P. Compo, Wesley Ebisuzaki, Ulrike Falk, Frank Fell, John Forsythe, Hans Hersbach, Misako Kachi, Shinya Kobayashi, Robert E. Kursinski, Diego Loyola, Zhengzao Luo, Johannes K. Nielsen, Enzo Papandrea, Laurence Picon, Rene Preusker, Anthony Reale, Lei Shi, Laura Slivinski, Joao Teixeira, Tom Vonder Haar, and Thomas Wagner
Atmos. Chem. Phys., 24, 9667–9695, https://doi.org/10.5194/acp-24-9667-2024, https://doi.org/10.5194/acp-24-9667-2024, 2024
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In a warmer future, water vapour will spend more time in the atmosphere, changing global rainfall patterns. In this study, we analysed the performance of 28 water vapour records between 1988 and 2014. We find sensitivity to surface warming generally outside expected ranges, attributed to breakpoints in individual record trends and differing representations of climate variability. The implication is that longer records are required for high confidence in assessing climate trends.
Gerrit Kuhlmann, Erik Koene, Sandro Meier, Diego Santaren, Grégoire Broquet, Frédéric Chevallier, Janne Hakkarainen, Janne Nurmela, Laia Amorós, Johanna Tamminen, and Dominik Brunner
Geosci. Model Dev., 17, 4773–4789, https://doi.org/10.5194/gmd-17-4773-2024, https://doi.org/10.5194/gmd-17-4773-2024, 2024
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We present a Python software library for data-driven emission quantification (ddeq). It can be used to determine the emissions of hot spots (cities, power plants and industry) from remote sensing images using different methods. ddeq can be extended for new datasets and methods, providing a powerful community tool for users and developers. The application of the methods is shown using Jupyter notebooks included in the library.
Robert P. Damadeo, Viktoria F. Sofieva, Alexei Rozanov, and Larry W. Thomason
Atmos. Meas. Tech., 17, 3669–3678, https://doi.org/10.5194/amt-17-3669-2024, https://doi.org/10.5194/amt-17-3669-2024, 2024
Short summary
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Comparing different aerosol data sets for scientific studies often requires converting aerosol extinction data between different wavelengths. A common approximation for the spectral behavior of aerosol is the Ångström formula; however, this introduces biases. Using measurements across many different wavelengths from a single instrument, we derive an empirical relationship to both characterize this bias and offer a correction for other studies that may employ this analysis approach.
Viktoria F. Sofieva, Monika Szelag, Johanna Tamminen, Didier Fussen, Christine Bingen, Filip Vanhellemont, Nina Mateshvili, Alexei Rozanov, and Christine Pohl
Atmos. Meas. Tech., 17, 3085–3101, https://doi.org/10.5194/amt-17-3085-2024, https://doi.org/10.5194/amt-17-3085-2024, 2024
Short summary
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We have developed the new multi-wavelength dataset of aerosol extinction profiles, which are retrieved from the averaged transmittance spectra by the Global Ozone Monitoring by Occultation of Stars instrument aboard Envisat. The retrieved aerosol extinction profiles are provided in the altitude range 10–40 km at 400, 440, 452, 470, 500, 525, 550, 672 and 750 nm for the period 2002–2012. FMI-GOMOSaero aerosol profiles have improved quality; they are in good agreement with other datasets.
Markku Kulmala, Anna Lintunen, Hanna Lappalainen, Annele Virtanen, Chao Yan, Ekaterina Ezhova, Tuomo Nieminen, Ilona Riipinen, Risto Makkonen, Johanna Tamminen, Anu-Maija Sundström, Antti Arola, Armin Hansel, Kari Lehtinen, Timo Vesala, Tuukka Petäjä, Jaana Bäck, Tom Kokkonen, and Veli-Matti Kerminen
Atmos. Chem. Phys., 23, 14949–14971, https://doi.org/10.5194/acp-23-14949-2023, https://doi.org/10.5194/acp-23-14949-2023, 2023
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To be able to meet global grand challenges, we need comprehensive open data with proper metadata. In this opinion paper, we describe the SMEAR (Station for Measuring Earth surface – Atmosphere Relations) concept and include several examples (cases), such as new particle formation and growth, feedback loops and the effect of COVID-19, and what has been learned from these investigations. The future needs and the potential of comprehensive observations of the environment are summarized.
Yingqi Zheng, Minttu Havu, Huizhi Liu, Xueling Cheng, Yifan Wen, Hei Shing Lee, Joyson Ahongshangbam, and Leena Järvi
Geosci. Model Dev., 16, 4551–4579, https://doi.org/10.5194/gmd-16-4551-2023, https://doi.org/10.5194/gmd-16-4551-2023, 2023
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The performance of the Surface Urban Energy and Water Balance Scheme (SUEWS) is evaluated against the observed surface exchanges (fluxes) of heat and carbon dioxide in a densely built neighborhood in Beijing. The heat flux modeling is noticeably improved by using the observed maximum conductance and by optimizing the vegetation phenology modeling. SUEWS also performs well in simulating carbon dioxide flux.
Ka Lok Chan, Pieter Valks, Klaus-Peter Heue, Ronny Lutz, Pascal Hedelt, Diego Loyola, Gaia Pinardi, Michel Van Roozendael, François Hendrick, Thomas Wagner, Vinod Kumar, Alkis Bais, Ankie Piters, Hitoshi Irie, Hisahiro Takashima, Yugo Kanaya, Yongjoo Choi, Kihong Park, Jihyo Chong, Alexander Cede, Udo Frieß, Andreas Richter, Jianzhong Ma, Nuria Benavent, Robert Holla, Oleg Postylyakov, Claudia Rivera Cárdenas, and Mark Wenig
Earth Syst. Sci. Data, 15, 1831–1870, https://doi.org/10.5194/essd-15-1831-2023, https://doi.org/10.5194/essd-15-1831-2023, 2023
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This paper presents the theoretical basis as well as verification and validation of the Global Ozone Monitoring Experiment-2 (GOME-2) daily and monthly level-3 products.
Viktoria F. Sofieva, Monika Szelag, Johanna Tamminen, Carlo Arosio, Alexei Rozanov, Mark Weber, Doug Degenstein, Adam Bourassa, Daniel Zawada, Michael Kiefer, Alexandra Laeng, Kaley A. Walker, Patrick Sheese, Daan Hubert, Michel van Roozendael, Christian Retscher, Robert Damadeo, and Jerry D. Lumpe
Atmos. Meas. Tech., 16, 1881–1899, https://doi.org/10.5194/amt-16-1881-2023, https://doi.org/10.5194/amt-16-1881-2023, 2023
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The paper presents the updated SAGE-CCI-OMPS+ climate data record of monthly zonal mean ozone profiles. This dataset covers the stratosphere and combines measurements by nine limb and occultation satellite instruments (SAGE II, OSIRIS, MIPAS, SCIAMACHY, GOMOS, ACE-FTS, OMPS-LP, POAM III, and SAGE III/ISS). The update includes new versions of MIPAS, ACE-FTS, and OSIRIS datasets and introduces data from additional sensors (POAM III and SAGE III/ISS) and retrieval processors (OMPS-LP).
Flora Kluge, Tilman Hüneke, Christophe Lerot, Simon Rosanka, Meike K. Rotermund, Domenico Taraborrelli, Benjamin Weyland, and Klaus Pfeilsticker
Atmos. Chem. Phys., 23, 1369–1401, https://doi.org/10.5194/acp-23-1369-2023, https://doi.org/10.5194/acp-23-1369-2023, 2023
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Using airborne glyoxal concentration and vertical column density measurements, vertical profiles are inferred for eight global regions in aged biomass burning plumes and the tropical marine boundary layer. Using TROPOMI observations, an analysis of space- and airborne measurements is performed. A comparison to EMAC simulations shows a general glyoxal underprediction, which points to various missing sources and precursors from anthropogenic activities, biomass burning, and the sea surface.
Katerina Garane, Ka Lok Chan, Maria-Elissavet Koukouli, Diego Loyola, and Dimitris Balis
Atmos. Meas. Tech., 16, 57–74, https://doi.org/10.5194/amt-16-57-2023, https://doi.org/10.5194/amt-16-57-2023, 2023
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In this work, 2.5 years of TROPOMI/S5P Total Column Water Vapor (TCWV) observations retrieved from the blue wavelength band are validated against co-located precipitable water measurements from NASA AERONET, which uses Cimel Sun photometers globally. Overall, the TCWV product agrees well on a global scale with the ground-based dataset (Pearson correl. coefficient 0.909) and has a mean relative bias of −2.7 ± 4.9 % with respect to the AERONET observations for moderate albedo and cloudiness.
Miriam Latsch, Andreas Richter, Henk Eskes, Maarten Sneep, Ping Wang, Pepijn Veefkind, Ronny Lutz, Diego Loyola, Athina Argyrouli, Pieter Valks, Thomas Wagner, Holger Sihler, Michel van Roozendael, Nicolas Theys, Huan Yu, Richard Siddans, and John P. Burrows
Atmos. Meas. Tech., 15, 6257–6283, https://doi.org/10.5194/amt-15-6257-2022, https://doi.org/10.5194/amt-15-6257-2022, 2022
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The article investigates different S5P TROPOMI cloud retrieval algorithms for tropospheric trace gas retrievals. The cloud products show differences primarily over snow and ice and for scenes under sun glint. Some issues regarding across-track dependence are found for the cloud fractions as well as for the cloud heights.
Klaus-Peter Heue, Diego Loyola, Fabian Romahn, Walter Zimmer, Simon Chabrillat, Quentin Errera, Jerry Ziemke, and Natalya Kramarova
Atmos. Meas. Tech., 15, 5563–5579, https://doi.org/10.5194/amt-15-5563-2022, https://doi.org/10.5194/amt-15-5563-2022, 2022
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To retrieve tropospheric ozone column information, we subtract stratospheric column data of BASCOE from TROPOMI/S5P total ozone columns.
The new S5P-BASCOE data agree well with existing tropospheric data like OMPS-MERRA-2. The data are also compared to ozone soundings.
The tropospheric ozone columns show the expected temporal and spatial patterns. We will also apply the algorithm to future UV nadir missions like Sentinel 4 or 5 or to recent and ongoing missions like GOME_2 or OMI.
Chao Yan, Yicheng Shen, Dominik Stolzenburg, Lubna Dada, Ximeng Qi, Simo Hakala, Anu-Maija Sundström, Yishuo Guo, Antti Lipponen, Tom V. Kokkonen, Jenni Kontkanen, Runlong Cai, Jing Cai, Tommy Chan, Liangduo Chen, Biwu Chu, Chenjuan Deng, Wei Du, Xiaolong Fan, Xu-Cheng He, Juha Kangasluoma, Joni Kujansuu, Mona Kurppa, Chang Li, Yiran Li, Zhuohui Lin, Yiliang Liu, Yuliang Liu, Yiqun Lu, Wei Nie, Jouni Pulliainen, Xiaohui Qiao, Yonghong Wang, Yifan Wen, Ye Wu, Gan Yang, Lei Yao, Rujing Yin, Gen Zhang, Shaojun Zhang, Feixue Zheng, Ying Zhou, Antti Arola, Johanna Tamminen, Pauli Paasonen, Yele Sun, Lin Wang, Neil M. Donahue, Yongchun Liu, Federico Bianchi, Kaspar R. Daellenbach, Douglas R. Worsnop, Veli-Matti Kerminen, Tuukka Petäjä, Aijun Ding, Jingkun Jiang, and Markku Kulmala
Atmos. Chem. Phys., 22, 12207–12220, https://doi.org/10.5194/acp-22-12207-2022, https://doi.org/10.5194/acp-22-12207-2022, 2022
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Atmospheric new particle formation (NPF) is a dominant source of atmospheric ultrafine particles. In urban environments, traffic emissions are a major source of primary pollutants, but their contribution to NPF remains under debate. During the COVID-19 lockdown, traffic emissions were significantly reduced, providing a unique chance to examine their relevance to NPF. Based on our comprehensive measurements, we demonstrate that traffic emissions alone are not able to explain the NPF in Beijing.
Sophie Godin-Beekmann, Niramson Azouz, Viktoria F. Sofieva, Daan Hubert, Irina Petropavlovskikh, Peter Effertz, Gérard Ancellet, Doug A. Degenstein, Daniel Zawada, Lucien Froidevaux, Stacey Frith, Jeannette Wild, Sean Davis, Wolfgang Steinbrecht, Thierry Leblanc, Richard Querel, Kleareti Tourpali, Robert Damadeo, Eliane Maillard Barras, René Stübi, Corinne Vigouroux, Carlo Arosio, Gerald Nedoluha, Ian Boyd, Roeland Van Malderen, Emmanuel Mahieu, Dan Smale, and Ralf Sussmann
Atmos. Chem. Phys., 22, 11657–11673, https://doi.org/10.5194/acp-22-11657-2022, https://doi.org/10.5194/acp-22-11657-2022, 2022
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An updated evaluation up to 2020 of stratospheric ozone profile long-term trends at extrapolar latitudes based on satellite and ground-based records is presented. Ozone increase in the upper stratosphere is confirmed, with significant trends at most latitudes. In this altitude region, a very good agreement is found with trends derived from chemistry–climate model simulations. Observed and modelled trends diverge in the lower stratosphere, but the differences are non-significant.
Niilo Kalakoski, Viktoria F. Sofieva, René Preusker, Claire Henocq, Matthieu Denisselle, Steffen Dransfeld, and Silvia Scifoni
Atmos. Meas. Tech., 15, 5129–5140, https://doi.org/10.5194/amt-15-5129-2022, https://doi.org/10.5194/amt-15-5129-2022, 2022
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Geophysical validation of the Integrated Water Vapour (IWV) product from the Sentinel-3 Ocean and Land Colour Instrument (OLCI) was performed against reference observations from SUOMINET and IGRA databases. Results for cloud-free matchups over land show a wet bias of 7 %–10 % for OLCI, with a high correlation against the reference observations (0.98 against SUOMINET and 0.90 against IGRA). Special attention is given to validation of uncertainty estimates and cloud flagging.
Nicolas Theys, Christophe Lerot, Hugues Brenot, Jeroen van Gent, Isabelle De Smedt, Lieven Clarisse, Mike Burton, Matthew Varnam, Catherine Hayer, Benjamin Esse, and Michel Van Roozendael
Atmos. Meas. Tech., 15, 4801–4817, https://doi.org/10.5194/amt-15-4801-2022, https://doi.org/10.5194/amt-15-4801-2022, 2022
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Sulfur dioxide plume height after a volcanic eruption is an important piece of information for many different scientific studies and applications. Satellite UV retrievals are useful in this respect, but available algorithms have shown so far limited sensitivity to SO2 height. Here we present a new technique to improve the retrieval of SO2 plume height for SO2 columns as low as 5 DU. We demonstrate the algorithm using TROPOMI measurements and compare with other height estimates.
Pieternel F. Levelt, Deborah C. Stein Zweers, Ilse Aben, Maite Bauwens, Tobias Borsdorff, Isabelle De Smedt, Henk J. Eskes, Christophe Lerot, Diego G. Loyola, Fabian Romahn, Trissevgeni Stavrakou, Nicolas Theys, Michel Van Roozendael, J. Pepijn Veefkind, and Tijl Verhoelst
Atmos. Chem. Phys., 22, 10319–10351, https://doi.org/10.5194/acp-22-10319-2022, https://doi.org/10.5194/acp-22-10319-2022, 2022
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Using the COVID-19 lockdown periods as an example, we show how Sentinel-5P/TROPOMI trace gas data (NO2, SO2, CO, HCHO and CHOCHO) can be used to understand impacts on air quality for regions and cities around the globe. We also provide information for both experienced and inexperienced users about how we created the data using state-of-the-art algorithms, where to get the data, methods taking meteorological and seasonal variability into consideration, and insights for future studies.
Francisco J. Pérez-Invernón, Heidi Huntrieser, Thilo Erbertseder, Diego Loyola, Pieter Valks, Song Liu, Dale J. Allen, Kenneth E. Pickering, Eric J. Bucsela, Patrick Jöckel, Jos van Geffen, Henk Eskes, Sergio Soler, Francisco J. Gordillo-Vázquez, and Jeff Lapierre
Atmos. Meas. Tech., 15, 3329–3351, https://doi.org/10.5194/amt-15-3329-2022, https://doi.org/10.5194/amt-15-3329-2022, 2022
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Lightning, one of the major sources of nitrogen oxides in the atmosphere, contributes to the tropospheric concentration of ozone and to the oxidizing capacity of the atmosphere. In this work, we contribute to improving the estimation of lightning-produced nitrogen oxides in the Ebro Valley and the Pyrenees by using two different TROPOMI products and comparing the results.
Viktoria F. Sofieva, Risto Hänninen, Mikhail Sofiev, Monika Szeląg, Hei Shing Lee, Johanna Tamminen, and Christian Retscher
Atmos. Meas. Tech., 15, 3193–3212, https://doi.org/10.5194/amt-15-3193-2022, https://doi.org/10.5194/amt-15-3193-2022, 2022
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We present tropospheric ozone column datasets that have been created using combinations of total ozone column from OMI and TROPOMI with stratospheric ozone column datasets from several available limb-viewing instruments (MLS, OSIRIS, MIPAS, SCIAMACHY, OMPS-LP, GOMOS). The main results are (i) several methodological developments, (ii) new tropospheric ozone column datasets from OMI and TROPOMI, and (iii) a new high-resolution dataset of ozone profiles from limb satellite instruments.
Melanie Coldewey-Egbers, Diego G. Loyola, Christophe Lerot, and Michel Van Roozendael
Atmos. Chem. Phys., 22, 6861–6878, https://doi.org/10.5194/acp-22-6861-2022, https://doi.org/10.5194/acp-22-6861-2022, 2022
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Monitoring the long-term evolution of ozone and the evaluation of trends is essential to assess the efficacy of the Montreal Protocol and its amendments. The first signs of recovery as a consequence of decreasing amounts of ozone-depleting substances have been reported, but the impact needs to be investigated in more detail. In the Southern Hemisphere significant positive trends were found, but in the Northern Hemisphere the expected increase is still not yet visible.
Mark Weber, Carlo Arosio, Melanie Coldewey-Egbers, Vitali E. Fioletov, Stacey M. Frith, Jeannette D. Wild, Kleareti Tourpali, John P. Burrows, and Diego Loyola
Atmos. Chem. Phys., 22, 6843–6859, https://doi.org/10.5194/acp-22-6843-2022, https://doi.org/10.5194/acp-22-6843-2022, 2022
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Long-term trends in column ozone have been determined from five merged total ozone datasets spanning the period 1978–2020. We show that ozone recovery due to the decline in stratospheric halogens after the 1990s (as regulated by the Montreal Protocol) is evident outside the tropical region and amounts to half a percent per decade. The ozone recovery in the Northern Hemisphere is however compensated for by the negative long-term trend contribution from atmospheric dynamics since the year 2000.
Maria-Elissavet Koukouli, Konstantinos Michailidis, Pascal Hedelt, Isabelle A. Taylor, Antje Inness, Lieven Clarisse, Dimitris Balis, Dmitry Efremenko, Diego Loyola, Roy G. Grainger, and Christian Retscher
Atmos. Chem. Phys., 22, 5665–5683, https://doi.org/10.5194/acp-22-5665-2022, https://doi.org/10.5194/acp-22-5665-2022, 2022
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Volcanic eruptions eject large amounts of ash and trace gases into the atmosphere. The use of space-borne instruments enables the global monitoring of volcanic SO2 emissions in an economical and risk-free manner. The main aim of this paper is to present its extensive verification, accomplished within the ESA S5P+I: SO2LH project, over major recent volcanic eruptions, against collocated space-borne measurements, as well as assess its impact on the forecasts provided by CAMS.
Antje Inness, Melanie Ades, Dimitris Balis, Dmitry Efremenko, Johannes Flemming, Pascal Hedelt, Maria-Elissavet Koukouli, Diego Loyola, and Roberto Ribas
Geosci. Model Dev., 15, 971–994, https://doi.org/10.5194/gmd-15-971-2022, https://doi.org/10.5194/gmd-15-971-2022, 2022
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This paper describes the way that the Copernicus Atmosphere Monitoring Service (CAMS) produces forecasts of volcanic SO2. These forecasts are provided routinely every day. They are created by blending SO2 data from satellite instruments (TROPOMI and GOME-2) with the CAMS model. We show that the quality of the CAMS SO2 forecasts can be improved if additional information about the height of volcanic plumes is provided in the satellite data.
Christophe Lerot, François Hendrick, Michel Van Roozendael, Leonardo M. A. Alvarado, Andreas Richter, Isabelle De Smedt, Nicolas Theys, Jonas Vlietinck, Huan Yu, Jeroen Van Gent, Trissevgeni Stavrakou, Jean-François Müller, Pieter Valks, Diego Loyola, Hitoshi Irie, Vinod Kumar, Thomas Wagner, Stefan F. Schreier, Vinayak Sinha, Ting Wang, Pucai Wang, and Christian Retscher
Atmos. Meas. Tech., 14, 7775–7807, https://doi.org/10.5194/amt-14-7775-2021, https://doi.org/10.5194/amt-14-7775-2021, 2021
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Global measurements of glyoxal tropospheric columns from the satellite instrument TROPOMI are presented. Such measurements can contribute to the estimation of atmospheric emissions of volatile organic compounds. This new glyoxal product has been fully characterized with a comprehensive error budget, with comparison with other satellite data sets as well as with validation based on independent ground-based remote sensing glyoxal observations.
Daan Hubert, Klaus-Peter Heue, Jean-Christopher Lambert, Tijl Verhoelst, Marc Allaart, Steven Compernolle, Patrick D. Cullis, Angelika Dehn, Christian Félix, Bryan J. Johnson, Arno Keppens, Debra E. Kollonige, Christophe Lerot, Diego Loyola, Matakite Maata, Sukarni Mitro, Maznorizan Mohamad, Ankie Piters, Fabian Romahn, Henry B. Selkirk, Francisco R. da Silva, Ryan M. Stauffer, Anne M. Thompson, J. Pepijn Veefkind, Holger Vömel, Jacquelyn C. Witte, and Claus Zehner
Atmos. Meas. Tech., 14, 7405–7433, https://doi.org/10.5194/amt-14-7405-2021, https://doi.org/10.5194/amt-14-7405-2021, 2021
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We assess the first 2 years of TROPOMI tropical tropospheric ozone column data. Comparisons to reference measurements by ozonesonde and satellite sensors show that TROPOMI bias (−0.1 to +2.3 DU) and precision (1.5 to 2.5 DU) meet mission requirements. Potential causes of bias and its spatio-temporal structure are discussed, as well as ways to identify sampling errors. Our analysis of known geophysical patterns demonstrates the improved performance of TROPOMI with respect to its predecessors.
Song Liu, Pieter Valks, Gaia Pinardi, Jian Xu, Ka Lok Chan, Athina Argyrouli, Ronny Lutz, Steffen Beirle, Ehsan Khorsandi, Frank Baier, Vincent Huijnen, Alkiviadis Bais, Sebastian Donner, Steffen Dörner, Myrto Gratsea, François Hendrick, Dimitris Karagkiozidis, Kezia Lange, Ankie J. M. Piters, Julia Remmers, Andreas Richter, Michel Van Roozendael, Thomas Wagner, Mark Wenig, and Diego G. Loyola
Atmos. Meas. Tech., 14, 7297–7327, https://doi.org/10.5194/amt-14-7297-2021, https://doi.org/10.5194/amt-14-7297-2021, 2021
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In this work, an improved tropospheric NO2 retrieval algorithm from TROPOMI measurements over Europe is presented. The stratospheric estimation is implemented with correction for the dependency of the stratospheric NO2 on the viewing geometry. The AMF calculation is implemented using improved surface albedo, a priori NO2 profiles, and cloud correction. The improved tropospheric NO2 data show good correlations with ground-based MAX-DOAS measurements.
Nicolas Theys, Vitali Fioletov, Can Li, Isabelle De Smedt, Christophe Lerot, Chris McLinden, Nickolay Krotkov, Debora Griffin, Lieven Clarisse, Pascal Hedelt, Diego Loyola, Thomas Wagner, Vinod Kumar, Antje Innes, Roberto Ribas, François Hendrick, Jonas Vlietinck, Hugues Brenot, and Michel Van Roozendael
Atmos. Chem. Phys., 21, 16727–16744, https://doi.org/10.5194/acp-21-16727-2021, https://doi.org/10.5194/acp-21-16727-2021, 2021
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We present a new algorithm to retrieve sulfur dioxide from space UV measurements. We apply the technique to high-resolution TROPOMI measurements and demonstrate the high sensitivity of the approach to weak SO2 emissions worldwide with an unprecedented limit of detection of 8 kt yr−1. This result has broad implications for atmospheric science studies dealing with improving emission inventories and identifying and quantifying missing sources, in the context of air quality and climate.
Anu Kauppi, Antti Kukkurainen, Antti Lipponen, Marko Laine, Antti Arola, Hannakaisa Lindqvist, and Johanna Tamminen
Atmos. Meas. Tech. Discuss., https://doi.org/10.5194/amt-2021-328, https://doi.org/10.5194/amt-2021-328, 2021
Revised manuscript not accepted
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We present a methodology in Bayesian framework for retrieving atmospheric aerosol optical depth and aerosol type from the pre-computed look-up tables (LUTs). Especially, we consider Bayesian model averaging and uncertainty originating from aerosol model selection and imperfect forward modelling. Our aim is to get more realistic uncertainty estimates. We have applied the methodology to TROPOMI/S5P satellite observations and evaluated the results against ground-based data from the AERONET.
Isabelle De Smedt, Gaia Pinardi, Corinne Vigouroux, Steven Compernolle, Alkis Bais, Nuria Benavent, Folkert Boersma, Ka-Lok Chan, Sebastian Donner, Kai-Uwe Eichmann, Pascal Hedelt, François Hendrick, Hitoshi Irie, Vinod Kumar, Jean-Christopher Lambert, Bavo Langerock, Christophe Lerot, Cheng Liu, Diego Loyola, Ankie Piters, Andreas Richter, Claudia Rivera Cárdenas, Fabian Romahn, Robert George Ryan, Vinayak Sinha, Nicolas Theys, Jonas Vlietinck, Thomas Wagner, Ting Wang, Huan Yu, and Michel Van Roozendael
Atmos. Chem. Phys., 21, 12561–12593, https://doi.org/10.5194/acp-21-12561-2021, https://doi.org/10.5194/acp-21-12561-2021, 2021
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This paper assess the performances of the TROPOMI formaldehyde observations compared to its predecessor OMI at different spatial and temporal scales. We also use a global network of MAX-DOAS instruments to validate both satellite datasets for a large range of HCHO columns. The precision obtained with daily TROPOMI observations is comparable to monthly OMI observations. We present clear detection of weak HCHO column enhancements related to shipping emissions in the Indian Ocean.
Antti Arola, William Wandji Nyamsi, Antti Lipponen, Stelios Kazadzis, Nickolay A. Krotkov, and Johanna Tamminen
Atmos. Meas. Tech., 14, 4947–4957, https://doi.org/10.5194/amt-14-4947-2021, https://doi.org/10.5194/amt-14-4947-2021, 2021
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Methods to estimate surface UV radiation from satellite measurements offer the only means to obtain global coverage, and the development of satellite-based UV algorithms has been ongoing since the early 1990s. One of the main challenges in this development has been how to account for the overall effect of absorption by atmospheric aerosols. One such method was suggested roughly a decade ago, and in this study we propose further improvements for this kind of approach.
Nikita M. Fedkin, Can Li, Nickolay A. Krotkov, Pascal Hedelt, Diego G. Loyola, Russell R. Dickerson, and Robert Spurr
Atmos. Meas. Tech., 14, 3673–3691, https://doi.org/10.5194/amt-14-3673-2021, https://doi.org/10.5194/amt-14-3673-2021, 2021
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This study presents a new volcanic sulfur dioxide (SO2) layer height retrieval algorithm for the Ozone Monitoring Instrument (OMI). We generated a large spectral dataset with a radiative transfer model and used it to train neural networks to predict SO2 height from OMI radiance data. The algorithm is fast and takes less than 10 min for a single orbit. Retrievals were tested on four eruption cases, and results had reasonable agreement (within 2 km) with other retrievals and previous studies.
Viktoria F. Sofieva, Monika Szeląg, Johanna Tamminen, Erkki Kyrölä, Doug Degenstein, Chris Roth, Daniel Zawada, Alexei Rozanov, Carlo Arosio, John P. Burrows, Mark Weber, Alexandra Laeng, Gabriele P. Stiller, Thomas von Clarmann, Lucien Froidevaux, Nathaniel Livesey, Michel van Roozendael, and Christian Retscher
Atmos. Chem. Phys., 21, 6707–6720, https://doi.org/10.5194/acp-21-6707-2021, https://doi.org/10.5194/acp-21-6707-2021, 2021
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The MErged GRIdded Dataset of Ozone Profiles is a long-term (2001–2018) stratospheric ozone profile climate data record with resolved longitudinal structure that combines the data from six limb satellite instruments. The dataset can be used for various analyses, some of which are discussed in the paper. In particular, regionally and vertically resolved ozone trends are evaluated, including trends in the polar regions.
Steven Compernolle, Athina Argyrouli, Ronny Lutz, Maarten Sneep, Jean-Christopher Lambert, Ann Mari Fjæraa, Daan Hubert, Arno Keppens, Diego Loyola, Ewan O'Connor, Fabian Romahn, Piet Stammes, Tijl Verhoelst, and Ping Wang
Atmos. Meas. Tech., 14, 2451–2476, https://doi.org/10.5194/amt-14-2451-2021, https://doi.org/10.5194/amt-14-2451-2021, 2021
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The high-resolution satellite Sentinel-5p TROPOMI observes several atmospheric gases. To account for cloud interference with the observations, S5P cloud data products (CLOUD OCRA/ROCINN_CAL, OCRA/ROCINN_CRB, and FRESCO) provide vital input: cloud fraction, cloud height, and cloud optical thickness. Here, S5P cloud parameters are validated by comparing with other satellite sensors (VIIRS, MODIS, and OMI) and with ground-based CloudNet data. The agreement depends on product type and cloud height.
Emily M. Gordon, Annika Seppälä, Bernd Funke, Johanna Tamminen, and Kaley A. Walker
Atmos. Chem. Phys., 21, 2819–2836, https://doi.org/10.5194/acp-21-2819-2021, https://doi.org/10.5194/acp-21-2819-2021, 2021
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Energetic particle precipitation (EPP) is the rain of solar energetic particles into the Earth's atmosphere. EPP is known to deplete O3 in the polar mesosphere–upper stratosphere via the formation of NOx. NOx also causes chlorine deactivation in the lower stratosphere and has, thus, been proposed to potentially result in reduced ozone depletion in the spring. We provide the first evidence to show that NOx formed by EPP is able to remove active chlorine, resulting in enhanced total ozone column.
Martin Dameris, Diego G. Loyola, Matthias Nützel, Melanie Coldewey-Egbers, Christophe Lerot, Fabian Romahn, and Michel van Roozendael
Atmos. Chem. Phys., 21, 617–633, https://doi.org/10.5194/acp-21-617-2021, https://doi.org/10.5194/acp-21-617-2021, 2021
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Record low ozone values were observed in March 2020. Dynamical and chemical circumstances leading to low ozone values in spring 2020 are discussed and are compared to similar dynamical conditions in the Northern Hemisphere in 1996/1997 and 2010/2011. 2019/2020 showed an unusual persistent polar vortex with low stratospheric temperatures, which were permanently below 195 K at 50 hPa. This enabled enhanced formation of polar stratospheric clouds and a subsequent clear reduction of total ozone.
Kaisa Lakkala, Jukka Kujanpää, Colette Brogniez, Nicolas Henriot, Antti Arola, Margit Aun, Frédérique Auriol, Alkiviadis F. Bais, Germar Bernhard, Veerle De Bock, Maxime Catalfamo, Christine Deroo, Henri Diémoz, Luca Egli, Jean-Baptiste Forestier, Ilias Fountoulakis, Katerina Garane, Rosa Delia Garcia, Julian Gröbner, Seppo Hassinen, Anu Heikkilä, Stuart Henderson, Gregor Hülsen, Bjørn Johnsen, Niilo Kalakoski, Angelos Karanikolas, Tomi Karppinen, Kevin Lamy, Sergio F. León-Luis, Anders V. Lindfors, Jean-Marc Metzger, Fanny Minvielle, Harel B. Muskatel, Thierry Portafaix, Alberto Redondas, Ricardo Sanchez, Anna Maria Siani, Tove Svendby, and Johanna Tamminen
Atmos. Meas. Tech., 13, 6999–7024, https://doi.org/10.5194/amt-13-6999-2020, https://doi.org/10.5194/amt-13-6999-2020, 2020
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The TROPOspheric Monitoring Instrument (TROPOMI) onboard the Sentinel-5 Precursor (S5P) satellite was launched on 13 October 2017 to provide the atmospheric composition for atmosphere and climate research. Ground-based data from 25 sites located in Arctic, subarctic, temperate, equatorial and Antarctic
areas were used for the validation of the TROPOMI surface ultraviolet (UV) radiation product. For most sites 60 %–80 % of TROPOMI data was within ± 20 % of ground-based data.
Omar Torres, Hiren Jethva, Changwoo Ahn, Glen Jaross, and Diego G. Loyola
Atmos. Meas. Tech., 13, 6789–6806, https://doi.org/10.5194/amt-13-6789-2020, https://doi.org/10.5194/amt-13-6789-2020, 2020
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TROPOMI measures the quantity of small suspended particles (aerosols). We describe initial results of aerosol measurements using a NASA algorithm that retrieves the UV aerosol index, aerosol optical depth, and single-scattering albedo. An evaluation of derived products using sun-photometer observations shows close agreement. We also use these results to discuss important biomass burning and wildfire events around the world that got the attention of scientists and news media alike.
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Short summary
Our paper discusses the structure function method, which allows validation of random uncertainties in the data and, at the same time, probing of the small-scale natural variability. We applied this method to the clear-sky total ozone measurements by TROPOMI Sentinel-5P satellite instrument and found that the TROPOMI random error estimation is adequate. The discussed method is a powerful tool, which can be used in various applications.
Our paper discusses the structure function method, which allows validation of random...
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