Articles | Volume 24, issue 16
https://doi.org/10.5194/acp-24-9419-2024
https://doi.org/10.5194/acp-24-9419-2024
Technical note
 | 
28 Aug 2024
Technical note |  | 28 Aug 2024

Technical note: Posterior uncertainty estimation via a Monte Carlo procedure specialized for 4D-Var data assimilation

Michael Stanley, Mikael Kuusela, Brendan Byrne, and Junjie Liu

Related authors

Global Carbon Budget 2024
Pierre Friedlingstein, Michael O'Sullivan, Matthew W. Jones, Robbie M. Andrew, Judith Hauck, Peter Landschützer, Corinne Le Quéré, Hongmei Li, Ingrid T. Luijkx, Are Olsen, Glen P. Peters, Wouter Peters, Julia Pongratz, Clemens Schwingshackl, Stephen Sitch, Josep G. Canadell, Philippe Ciais, Robert B. Jackson, Simone R. Alin, Almut Arneth, Vivek Arora, Nicholas R. Bates, Meike Becker, Nicolas Bellouin, Carla F. Berghoff, Henry C. Bittig, Laurent Bopp, Patricia Cadule, Katie Campbell, Matthew A. Chamberlain, Naveen Chandra, Frédéric Chevallier, Louise P. Chini, Thomas Colligan, Jeanne Decayeux, Laique Djeutchouang, Xinyu Dou, Carolina Duran Rojas, Kazutaka Enyo, Wiley Evans, Amanda Fay, Richard A. Feely, Daniel J. Ford, Adrianna Foster, Thomas Gasser, Marion Gehlen, Thanos Gkritzalis, Giacomo Grassi, Luke Gregor, Nicolas Gruber, Özgür Gürses, Ian Harris, Matthew Hefner, Jens Heinke, George C. Hurtt, Yosuke Iida, Tatiana Ilyina, Andrew R. Jacobson, Atul Jain, Tereza Jarníková, Annika Jersild, Fei Jiang, Zhe Jin, Etsushi Kato, Ralph F. Keeling, Kees Klein Goldewijk, Jürgen Knauer, Jan Ivar Korsbakken, Siv K. Lauvset, Nathalie Lefèvre, Zhu Liu, Junjie Liu, Lei Ma, Shamil Maksyutov, Gregg Marland, Nicolas Mayot, Patrick McGuire, Nicolas Metzl, Natalie M. Monacci, Eric J. Morgan, Shin-Ichiro Nakaoka, Craig Neill, Yosuke Niwa, Tobias Nützel, Lea Olivier, Tsuneo Ono, Paul I. Palmer, Denis Pierrot, Zhangcai Qin, Laure Resplandy, Alizée Roobaert, Thais M. Rosan, Christian Rödenbeck, Jörg Schwinger, T. Luke Smallman, Stephen Smith, Reinel Sospedra-Alfonso, Tobias Steinhoff, Qing Sun, Adrienne J. Sutton, Roland Séférian, Shintaro Takao, Hiroaki Tatebe, Hanqin Tian, Bronte Tilbrook, Olivier Torres, Etienne Tourigny, Hiroyuki Tsujino, Francesco Tubiello, Guido van der Werf, Rik Wanninkhof, Xuhui Wang, Dongxu Yang, Xiaojuan Yang, Zhen Yu, Wenping Yuan, Xu Yue, Sönke Zaehle, Ning Zeng, and Jiye Zeng
Earth Syst. Sci. Data Discuss., https://doi.org/10.5194/essd-2024-519,https://doi.org/10.5194/essd-2024-519, 2024
Preprint under review for ESSD
Short summary
Upper-ocean changes with hurricane-strength wind events: a study using Argo profiles and an ocean reanalysis
Jacopo Sala, Donata Giglio, Addison Hu, Mikael Kuusela, Kimberly M. Wood, and Ann B. Lee
Ocean Sci., 20, 1441–1455, https://doi.org/10.5194/os-20-1441-2024,https://doi.org/10.5194/os-20-1441-2024, 2024
Short summary
Global Greenhouse Gas Reconciliation 2022
Zhu Deng, Philippe Ciais, Liting Hu, Adrien Martinez, Marielle Saunois, Rona L. Thompson, Kushal Tibrewal, Wouter Peters, Brendan Byrne, Giacomo Grassi, Paul I. Palmer, Ingrid T. Luijkx, Zhu Liu, Junjie Liu, Xuekun Fang, Tengjiao Wang, Hanqin Tian, Katsumasa Tanaka, Ana Bastos, Stephen Sitch, Benjamin Poulter, Clément Albergel, Aki Tsuruta, Shamil Maksyutov, Rajesh Janardanan, Yosuke Niwa, Bo Zheng, Joël Thanwerdas, Dmitry Belikov, Arjo Segers, and Frédéric Chevallier
Earth Syst. Sci. Data Discuss., https://doi.org/10.5194/essd-2024-103,https://doi.org/10.5194/essd-2024-103, 2024
Revised manuscript under review for ESSD
Short summary
The importance of digital elevation model accuracy in XCO2 retrievals: improving the Orbiting Carbon Observatory 2 Atmospheric Carbon Observations from Space version 11 retrieval product
Nicole Jacobs, Christopher W. O'Dell, Thomas E. Taylor, Thomas L. Logan, Brendan Byrne, Matthäus Kiel, Rigel Kivi, Pauli Heikkinen, Aronne Merrelli, Vivienne H. Payne, and Abhishek Chatterjee
Atmos. Meas. Tech., 17, 1375–1401, https://doi.org/10.5194/amt-17-1375-2024,https://doi.org/10.5194/amt-17-1375-2024, 2024
Short summary
Functional analysis of variance (ANOVA) for carbon flux estimates from remote sensing data
Jonathan Hobbs, Matthias Katzfuss, Hai Nguyen, Vineet Yadav, and Junjie Liu
Geosci. Model Dev., 17, 1133–1151, https://doi.org/10.5194/gmd-17-1133-2024,https://doi.org/10.5194/gmd-17-1133-2024, 2024
Short summary

Related subject area

Subject: Climate and Earth System | Research Activity: Atmospheric Modelling and Data Analysis | Altitude Range: Troposphere | Science Focus: Physics (physical properties and processes)
Constraining net long-term climate feedback from satellite-observed internal variability possible by the mid-2030s
Alejandro Uribe, Frida A.-M. Bender, and Thorsten Mauritsen
Atmos. Chem. Phys., 24, 13371–13384, https://doi.org/10.5194/acp-24-13371-2024,https://doi.org/10.5194/acp-24-13371-2024, 2024
Short summary
Investigation of the characteristics of low-level jets over North America in a convection-permitting Weather Research and Forecasting simulation
Xiao Ma, Yanping Li, Zhenhua Li, and Fei Huo
Atmos. Chem. Phys., 24, 12013–12030, https://doi.org/10.5194/acp-24-12013-2024,https://doi.org/10.5194/acp-24-12013-2024, 2024
Short summary
Impacts of tropical cyclone–heat wave compound events on surface ozone in eastern China: comparison between the Yangtze River and Pearl River deltas
Cuini Qi, Pinya Wang, Yang Yang, Huimin Li, Hui Zhang, Lili Ren, Xipeng Jin, Chenchao Zhan, Jianping Tang, and Hong Liao
Atmos. Chem. Phys., 24, 11775–11789, https://doi.org/10.5194/acp-24-11775-2024,https://doi.org/10.5194/acp-24-11775-2024, 2024
Short summary
The 2023 global warming spike was driven by the El Niño–Southern Oscillation
Shiv Priyam Raghuraman, Brian Soden, Amy Clement, Gabriel Vecchi, Sofia Menemenlis, and Wenchang Yang
Atmos. Chem. Phys., 24, 11275–11283, https://doi.org/10.5194/acp-24-11275-2024,https://doi.org/10.5194/acp-24-11275-2024, 2024
Short summary
Present-day methane shortwave absorption mutes surface warming relative to preindustrial conditions
Robert J. Allen, Xueying Zhao, Cynthia A. Randles, Ryan J. Kramer, Bjørn H. Samset, and Christopher J. Smith
Atmos. Chem. Phys., 24, 11207–11226, https://doi.org/10.5194/acp-24-11207-2024,https://doi.org/10.5194/acp-24-11207-2024, 2024
Short summary

Cited articles

Bey, I., Jacob, D. J., Yantosca, R. M., Logan, J. A., Field, B. D., Fiore, A. M., Li, Q., Liu, H. Y., Mickley, L. J., and Schultz, M. G.: Global modeling of tropospheric chemistry with assimilated meteorology: Model description and evaluation, J. Geophys. Res., 106, 23073–23095, https://doi.org/10.1029/2001JD000807, 2001 (code is available at http://wiki.seas.harvard.edu/geos-chem, last access: 9 October 2019). a, b
Bousserez, N. and Henze, D. K.: Optimal and scalable methods to approximate the solutions of large-scale Bayesian problems: theory and application to atmospheric inversion and data assimilation, Q. J. Roy. Meteorol. Soc., 144, 365–390, 2018. a
Byrd, R. H., Lu, P., Nocedal, J., and Zhu, C.: A limited memory algorithm for bound constrained optimization, SIAM J. Sci. Comput., 16, 1190–1208, 1995. a
Byrne, B., Jones, D. B. A., Strong, K., Polavarapu, S. M., Harper, A. B., Baker, D. F., and Maksyutov, S.: On what scales can GOSAT flux inversions constrain anomalies in terrestrial ecosystems?, Atmos. Chem. Phys., 19, 13017–13035, https://doi.org/10.5194/acp-19-13017-2019, 2019. a
Byrne, B., Baker, D. F., Basu, S., Bertolacci, M., Bowman, K. W., Carroll, D., Chatterjee, A., Chevallier, F., Ciais, P., Cressie, N., Crisp, D., Crowell, S., Deng, F., Deng, Z., Deutscher, N. M., Dubey, M. K., Feng, S., García, O. E., Griffith, D. W. T., Herkommer, B., Hu, L., Jacobson, A. R., Janardanan, R., Jeong, S., Johnson, M. S., Jones, D. B. A., Kivi, R., Liu, J., Liu, Z., Maksyutov, S., Miller, J. B., Miller, S. M., Morino, I., Notholt, J., Oda, T., O'Dell, C. W., Oh, Y.-S., Ohyama, H., Patra, P. K., Peiro, H., Petri, C., Philip, S., Pollard, D. F., Poulter, B., Remaud, M., Schuh, A., Sha, M. K., Shiomi, K., Strong, K., Sweeney, C., Té, Y., Tian, H., Velazco, V. A., Vrekoussis, M., Warneke, T., Worden, J. R., Wunch, D., Yao, Y., Yun, J., Zammit-Mangion, A., and Zeng, N.: National CO2 budgets (2015–2020) inferred from atmospheric CO2 observations in support of the global stocktake, Earth Syst. Sci. Data, 15, 963–1004, https://doi.org/10.5194/essd-15-963-2023, 2023. a
Download
Short summary
To serve the uncertainty quantification (UQ) needs of 4D-Var data assimilation (DA) practitioners, we describe and justify a UQ algorithm from carbon flux inversion and incorporate its sampling uncertainty into the final reported UQ. The algorithm is mathematically proved, and its performance is shown for a carbon flux observing system simulation experiment. These results legitimize and generalize this algorithm's current use and make available this effective algorithm to new DA domains.
Altmetrics
Final-revised paper
Preprint