Articles | Volume 17, issue 23
https://doi.org/10.5194/gmd-17-8853-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/gmd-17-8853-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
A joint reconstruction and model selection approach for large-scale linear inverse modeling (msHyBR v2)
Malena Sabaté Landman
Department of Mathematics, Emory University, Atlanta, GA, USA
Department of Mathematics, Emory University, Atlanta, GA, USA
Jiahua Jiang
School of Mathematics, University of Birmingham, Birmingham, UK
Scot M. Miller
Department of Environmental Health and Engineering, Johns Hopkins University, Baltimore, MD, USA
Arvind K. Saibaba
Department of Mathematics, North Carolina State University, Raleigh, NC, USA
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Hanyu Liu, Felix R. Vogel, Misa Ishizawa, Zhen Zhang, Benjamin Poulter, Doug E. J. Worthy, Leyang Feng, Anna L. Gagné-Landmann, Ao Chen, Ziting Huang, Dylan C. Gaeta, Joe R. Melton, Douglas Chan, Vineet Yadav, Deborah Huntzinger, and Scot M. Miller
EGUsphere, https://doi.org/10.5194/egusphere-2025-2150, https://doi.org/10.5194/egusphere-2025-2150, 2025
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We find that the state-of-the-art process-based methane flux models have both lower flux magnitude and reduced inter-model uncertainty compared to a previous model inter-comparison from over a decade ago. Despite these improvements, methane flux estimates from process-based models are still likely too high compared to atmospheric observations. We also find that models with simpler parameterizations often result in better agreement with atmospheric observations in high-latitude North America.
Brendan Byrne, David F. Baker, Sourish Basu, Michael Bertolacci, Kevin W. Bowman, Dustin Carroll, Abhishek Chatterjee, Frédéric Chevallier, Philippe Ciais, Noel Cressie, David Crisp, Sean Crowell, Feng Deng, Zhu Deng, Nicholas M. Deutscher, Manvendra K. Dubey, Sha Feng, Omaira E. García, David W. T. Griffith, Benedikt Herkommer, Lei Hu, Andrew R. Jacobson, Rajesh Janardanan, Sujong Jeong, Matthew S. Johnson, Dylan B. A. Jones, Rigel Kivi, Junjie Liu, Zhiqiang Liu, Shamil Maksyutov, John B. Miller, Scot M. Miller, Isamu Morino, Justus Notholt, Tomohiro Oda, Christopher W. O'Dell, Young-Suk Oh, Hirofumi Ohyama, Prabir K. Patra, Hélène Peiro, Christof Petri, Sajeev Philip, David F. Pollard, Benjamin Poulter, Marine Remaud, Andrew Schuh, Mahesh K. Sha, Kei Shiomi, Kimberly Strong, Colm Sweeney, Yao Té, Hanqin Tian, Voltaire A. Velazco, Mihalis Vrekoussis, Thorsten Warneke, John R. Worden, Debra Wunch, Yuanzhi Yao, Jeongmin Yun, Andrew Zammit-Mangion, and Ning Zeng
Earth Syst. Sci. Data, 15, 963–1004, https://doi.org/10.5194/essd-15-963-2023, https://doi.org/10.5194/essd-15-963-2023, 2023
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Changes in the carbon stocks of terrestrial ecosystems result in emissions and removals of CO2. These can be driven by anthropogenic activities (e.g., deforestation), natural processes (e.g., fires) or in response to rising CO2 (e.g., CO2 fertilization). This paper describes a dataset of CO2 emissions and removals derived from atmospheric CO2 observations. This pilot dataset informs current capabilities and future developments towards top-down monitoring and verification systems.
Taewon Cho, Julianne Chung, Scot M. Miller, and Arvind K. Saibaba
Geosci. Model Dev., 15, 5547–5565, https://doi.org/10.5194/gmd-15-5547-2022, https://doi.org/10.5194/gmd-15-5547-2022, 2022
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Atmospheric inverse modeling describes the process of estimating greenhouse gas fluxes or air pollution emissions at the Earth's surface using observations of these gases collected in the atmosphere. The launch of new satellites, the expansion of surface observation networks, and a desire for more detailed maps of surface fluxes have yielded numerous computational and statistical challenges. This article describes computationally efficient methods for large-scale atmospheric inverse modeling.
Xiaoling Liu, August L. Weinbren, He Chang, Jovan M. Tadić, Marikate E. Mountain, Michael E. Trudeau, Arlyn E. Andrews, Zichong Chen, and Scot M. Miller
Geosci. Model Dev., 14, 4683–4696, https://doi.org/10.5194/gmd-14-4683-2021, https://doi.org/10.5194/gmd-14-4683-2021, 2021
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Observations of greenhouse gases have become far more numerous in recent years due to new satellite observations. The sheer size of these datasets makes it challenging to incorporate these data into statistical models and use these data to estimate greenhouse gas sources and sinks. In this paper, we develop an approach to reduce the size of these datasets while preserving the most information possible. We subsequently test this approach using satellite observations of carbon dioxide.
Zichong Chen, Junjie Liu, Daven K. Henze, Deborah N. Huntzinger, Kelley C. Wells, Stephen Sitch, Pierre Friedlingstein, Emilie Joetzjer, Vladislav Bastrikov, Daniel S. Goll, Vanessa Haverd, Atul K. Jain, Etsushi Kato, Sebastian Lienert, Danica L. Lombardozzi, Patrick C. McGuire, Joe R. Melton, Julia E. M. S. Nabel, Benjamin Poulter, Hanqin Tian, Andrew J. Wiltshire, Sönke Zaehle, and Scot M. Miller
Atmos. Chem. Phys., 21, 6663–6680, https://doi.org/10.5194/acp-21-6663-2021, https://doi.org/10.5194/acp-21-6663-2021, 2021
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NASA's Orbiting Carbon Observatory 2 (OCO-2) satellite observes atmospheric CO2 globally. We use a multiple regression and inverse model to quantify the relationships between OCO-2 and environmental drivers within individual years for 2015–2018 and within seven global biomes. Our results point to limitations of current space-based observations for inferring environmental relationships but also indicate the potential to inform key relationships that are very uncertain in process-based models.
Cited articles
Bauer, F. and Lukas, M. A.: Comparing parameter choice methods for regularization of ill-posed problems, Math. Comput. Simulat., 81, 1795–1841, https://doi.org/10.1016/j.matcom.2011.01.016, 2011. a
Beck, A. and Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems, SIAM J. Imaging Sci., 2, 183–202, https://doi.org/10.1137/080716542, 2009. a
Björck, Å.: Numerical methods for least squares problems, SIAM, ISBN 978-0-89871-360-2, https://doi.org/10.1137/1.9781611971484, 1996. a
Bozdogan, H.: Model selection and Akaike's information criterion (AIC): The general theory and its analytical extensions, Psychometrika, 52, 345–370, 1987. a
Brasseur, G. P. and Jacob, D. J.: Inverse Modeling for Atmospheric Chemistry, 487–537, Cambridge University Press, https://doi.org/10.1017/9781316544754.012, 2017. a, b, c
Calvetti, D., Pragliola, M., Somersalo, E., and Strang, A.: Sparse reconstructions from few noisy data: analysis of hierarchical Bayesian models with generalized gamma hyperpriors, Inverse Problems, 36, 025010, https://doi.org/10.1088/1361-6420/ab4d92, 2020. a, b
Carvalho, C. M., Polson, N. G., and Scott, J. G.: The horseshoe estimator for sparse signals, Biometrika, 97, 465–480, 2010. a
Chen, Z., Huntzinger, D. N., Liu, J., Piao, S., Wang, X., Sitch, S., Friedlingstein, P., Anthoni, P., Arneth, A., Bastrikov, V., Goll, D. S., Haverd, V., Jain, A. K., Joetzjer, E., Kato, E., Lienert, S., Lombardozzi, D. L., McGuire, P. C., Melton, J. R., Nabel, J. E. M. S., Pongratz, J., Poulter, B., Tian, H., Wiltshire, A. J., Zaehle, S., and Miller, S. M.: Five years of variability in the global carbon cycle: comparing an estimate from the Orbiting Carbon Observatory-2 and process-based models, Environ. Res. Lett., 16, 054041, https://doi.org/10.1088/1748-9326/abfac1, 2021a. a, b, c
Chen, Z., Liu, J., Henze, D. K., Huntzinger, D. N., Wells, K. C., Sitch, S., Friedlingstein, P., Joetzjer, E., Bastrikov, V., Goll, D. S., Haverd, V., Jain, A. K., Kato, E., Lienert, S., Lombardozzi, D. L., McGuire, P. C., Melton, J. R., Nabel, J. E. M. S., Poulter, B., Tian, H., Wiltshire, A. J., Zaehle, S., and Miller, S. M.: Linking global terrestrial CO2 fluxes and environmental drivers: inferences from the Orbiting Carbon Observatory 2 satellite and terrestrial biospheric models, Atmos. Chem. Phys., 21, 6663–6680, https://doi.org/10.5194/acp-21-6663-2021, 2021b. a, b, c, d
Cho, T., Chung, J., and Jiang, J.: Hybrid Projection Methods for Large-scale Inverse Problems with Mixed Gaussian Priors, Inverse Problems, 37, 4, https://doi.org/10.1088/1361-6420/abd29d, 2020. a
Chung, J. and Gazzola, S.: Flexible Krylov Methods for ℓp Regularization, SIAM J. Sci. Comput., 41, S149–S171, 2019. a
Chung, J. and Gazzola, S.: Computational methods for large-scale inverse problems: a survey on hybrid projection methods, SIAM Review, 66, 205–284, https://doi.org/10.1137/21M1441420, 2024. a
Daubechies, I., DeVore, R., Fornasier, M., and Güntürk, C. S.: Iteratively reweighted least squares minimization for sparse recovery, Commun. Pure Appl. Math., 63, 1–38, https://doi.org/10.1002/cpa.20303, 2010. a
Enting, I. G.: Inverse Problems in Atmospheric Constituent Transport, Cambridge Atmospheric and Space Science Series, Cambridge University Press, https://doi.org/10.1017/CBO9780511535741, 2002. a
Fang, Y. and Michalak, A. M.: Atmospheric observations inform CO2 flux responses to enviroclimatic drivers, Global Biogeochem. Cycles, 29, 555–566, https://doi.org/10.1002/2014GB005034, 2015. a
Friedlingstein, P., O'Sullivan, M., Jones, M. W., Andrew, R. M., Gregor, L., Hauck, J., Le Quéré, C., Luijkx, I. T., Olsen, A., Peters, G. P., Peters, W., Pongratz, J., Schwingshackl, C., Sitch, S., Canadell, J. G., Ciais, P., Jackson, R. B., Alin, S. R., Alkama, R., Arneth, A., Arora, V. K., Bates, N. R., Becker, M., Bellouin, N., Bittig, H. C., Bopp, L., Chevallier, F., Chini, L. P., Cronin, M., Evans, W., Falk, S., Feely, R. A., Gasser, T., Gehlen, M., Gkritzalis, T., Gloege, L., Grassi, G., Gruber, N., Gürses, Ö., Harris, I., Hefner, M., Houghton, R. A., Hurtt, G. C., Iida, Y., Ilyina, T., Jain, A. K., Jersild, A., Kadono, K., Kato, E., Kennedy, D., Klein Goldewijk, K., Knauer, J., Korsbakken, J. I., Landschützer, P., Lefèvre, N., Lindsay, K., Liu, J., Liu, Z., Marland, G., Mayot, N., McGrath, M. J., Metzl, N., Monacci, N. M., Munro, D. R., Nakaoka, S.-I., Niwa, Y., O'Brien, K., Ono, T., Palmer, P. I., Pan, N., Pierrot, D., Pocock, K., Poulter, B., Resplandy, L., Robertson, E., Rödenbeck, C., Rodriguez, C., Rosan, T. M., Schwinger, J., Séférian, R., Shutler, J. D., Skjelvan, I., Steinhoff, T., Sun, Q., Sutton, A. J., Sweeney, C., Takao, S., Tanhua, T., Tans, P. P., Tian, X., Tian, H., Tilbrook, B., Tsujino, H., Tubiello, F., van der Werf, G. R., Walker, A. P., Wanninkhof, R., Whitehead, C., Willstrand Wranne, A., Wright, R., Yuan, W., Yue, C., Yue, X., Zaehle, S., Zeng, J., and Zheng, B.: Global Carbon Budget 2022, Earth Syst. Sci. Data, 14, 4811–4900, https://doi.org/10.5194/essd-14-4811-2022, 2022. a
Gazzola, S. and Sabaté Landman, M.: Krylov methods for inverse problems: Surveying classical, and introducing new, algorithmic approaches, GAMM-Mitteilungen, 43, e202000017, https://doi.org/10.1002/gamm.202000017, 2020. a
Gazzola, S., Nagy, J. G., and Landman, M. S.: Iteratively Reweighted FGMRES and FLSQR for Sparse Reconstruction, SIAM J. Sci. Comput., 43, S47–S69, https://doi.org/10.1137/20M1333948, 2021. a
Gourdji, S. M., Mueller, K. L., Schaefer, K., and Michalak, A. M.: Global monthly averaged CO2 fluxes recovered using a geostatistical inverse modeling approach: 2. Results including auxiliary environmental data, J. Geophys. Res.-Atmos., 113, https://doi.org/10.1029/2007JD009733, d21115, 2008. a, b, c, d, e
Gourdji, S. M., Mueller, K. L., Yadav, V., Huntzinger, D. N., Andrews, A. E., Trudeau, M., Petron, G., Nehrkorn, T., Eluszkiewicz, J., Henderson, J., Wen, D., Lin, J., Fischer, M., Sweeney, C., and Michalak, A. M.: North American CO2 exchange: inter-comparison of modeled estimates with results from a fine-scale atmospheric inversion, Biogeosciences, 9, 457–475, https://doi.org/10.5194/bg-9-457-2012, 2012. a, b, c, d
Hersbach, H., Bell, B., Berrisford, P., Hirahara, S., Horányi, A., Muñoz-Sabater, J., Nicolas, J., Peubey, C., Radu, R., Schepers, D., Simmons, A., Soci, C., Abdalla, S., Abellan, X., Balsamo, G., Bechtold, P., Biavati, G., Bidlot, J., Bonavita, M., De Chiara, G., Dahlgren, P., Dee, D., Diamantakis, M., Dragani, R., Flemming, J., Forbes, R., Fuentes, M., Geer, A., Haimberger, L., Healy, S., Hogan, R. J., Hólm, E., Janisková, M., Keeley, S., Laloyaux, P., Lopez, P., Lupu, C., Radnoti, G., de Rosnay, P., Rozum, I., Vamborg, F., Villaume, S., and Thépaut, J.-N.: The ERA5 global reanalysis, Q. J. Roy. Meteor. Soc., 146, 1999–2049, https://doi.org/10.1002/qj.3803, 2020. a
Jacobson, A. R., Schuldt, K. N., Tans, P., Arlyn Andrews, Miller, J. B., Oda, T., Mund, J., Weir, B., Ott, L., Aalto, T., Abshire, J. B., Aikin, K., Aoki, S., Apadula, F., Arnold, S., Baier, B., Bartyzel, J., Beyersdorf, A., Biermann, T., Biraud, S. C., Boenisch, H., Brailsford, G., Brand, W. A., Chen, G., Huilin Chen, Lukasz Chmura, Clark, S., Colomb, A., Commane, R., Conil, S., Couret, C., Cox, A., Cristofanelli, P., Cuevas, E., Curcoll, R., Daube, B., Davis, K. J., De Wekker, S., Coletta, J. D., Delmotte, M., DiGangi, E., DiGangi, J. P., Di Sarra, A. G., Dlugokencky, E., Elkins, J. W., Emmenegger, L., Shuangxi Fang, Fischer, M. L., Forster, G., Frumau, A., Galkowski, M., Gatti, L. V., Gehrlein, T., Gerbig, C., Francois Gheusi, Gloor, E., Gomez-Trueba, V., Goto, D., Griffis, T., Hammer, S., Hanson, C., Haszpra, L., Hatakka, J., Heimann, M., Heliasz, M., Hensen, A., Hermansen, O., Hintsa, E., Holst, J., Ivakhov, V., Jaffe, D. A., Jordan, A., Joubert, W., Karion, A., Kawa, S. R., Kazan, V., Keeling, R. F., Keronen, P., Kneuer, T., Kolari, P., Kateřina Komínková, Kort, E., Kozlova, E., Krummel, P., Kubistin, D., Labuschagne, C., Lam, D. H., Lan, X., Langenfelds, R. L., Laurent, O., Laurila, T., Lauvaux, T., Lavric, J., Law, B. E., Lee, J., Lee, O. S., Lehner, I., Lehtinen, K., Leppert, R., Leskinen, A., Leuenberger, M., Levin, I., Levula, J., Lin, J., Lindauer, M., Loh, Z., Lopez, M., Luijkx, I. T., Lunder, C. R., Machida, T., Mammarella, I., Manca, G., Manning, A., Manning, A., Marek, M. V., Martin, M. Y., Matsueda, H., McKain, K., Meijer, H., Meinhardt, F., Merchant, L., N. Mihalopoulos, Miles, N. L., Miller, C. E., Mitchell, L., Mölder, M., Montzka, S., Moore, F., Moossen, H., Morgan, E., Josep-Anton Morgui, Morimoto, S., Müller-Williams, J., J. William Munger, Munro, D., Myhre, C. L., Shin-Ichiro Nakaoka, Jaroslaw Necki, Newman, S., Nichol, S., Niwa, Y., Obersteiner, F., O'Doherty, S., Paplawsky, B., Peischl, J., Peltola, O., Piacentino, S., Jean-Marc Pichon, Pickers, P., Piper, S., Pitt, J., Plass-Dülmer, C., Platt, S. M., Prinzivalli, S., Ramonet, M., Ramos, R., Reyes-Sanchez, E., Richardson, S. J., Riris, H., Rivas, P. P., Ryerson, T., Saito, K., Sargent, M., Sasakawa, M., Scheeren, B., Schuck, T., Schumacher, M., Seifert, T., Sha, M. K., Shepson, P., Shook, M., Sloop, C. D., Smith, P., Stanley, K., Steinbacher, M., Stephens, B., Sweeney, C., Thoning, K., Timas, H., Torn, M., Tørseth, K., Trisolino, P., Turnbull, J., Van Den Bulk, P., Van Dinther, D., Vermeulen, A., Viner, B., Vitkova, G., Walker, S., Watson, A., Wofsy, S. C., Worsey, J., Worthy, D., Dickon Young, Zaehle, S., Zahn, A., and Zimnoch, M.: CarbonTracker CT2022, https://doi.org/10.25925/Z1GJ-3254, 2023. a, b
Kilmer, M. E. and O'Leary, D. P.: Choosing Regularization Parameters in Iterative Methods for Ill-Posed Problems, SIAM J. Matrix Anal. A., 22, 1204–1221, 2001. a
Kitanidis, P. K.: A variance-ratio test for supporting a variable mean in kriging, Math. Geol., 29, 335–348, https://doi.org/10.1007/BF02769639, 1997. a
Kitanidis, P. K. and VoMvoris, E. G.: A geostatistical approach to the inverse problem in groundwater modeling (steady state) and one-dimensional simulations, Water Resour. Res., 19, 677–690, https://doi.org/10.1029/WR019i003p00677, 1983. a, b
Landman, M. S., Chung, J., and Saibaba, A. K.: Inverse-Modeling/msHyBR: Version 2, Zenodo [software], https://doi.org/10.5281/zenodo.11622130, 2024. a, b
Lin, J. C., Gerbig, C., Wofsy, S. C., Andrews, A. E., Daube, B. C., Davis, K. J., and Grainger, C. A.: A near-field tool for simulating the upstream influence of atmospheric observations: The Stochastic Time-Inverted Lagrangian Transport (STILT) model, J. Geophys. Res.-Atmos., 108, 4493, https://doi.org/10.1029/2002JD003161, 2003. a
Liu, X., Weinbren, A. L., Chang, H., Tadić, J. M., Mountain, M. E., Trudeau, M. E., Andrews, A. E., Chen, Z., and Miller, S. M.: Data reduction for inverse modeling: an adaptive approach v1.0, Geosci. Model Dev., 14, 4683–4696, https://doi.org/10.5194/gmd-14-4683-2021, 2021. a, b
Michalak, A. M., Bruhwiler, L., and Tans, P. P.: A geostatistical approach to surface flux estimation of atmospheric trace gases, J. Geophys. Res.-Atmos., 109, D14109, https://doi.org/10.1029/2003JD004422, 2004. a, b, c
Miller, S. M., Wofsy, S. C., Michalak, A. M., Kort, E. A., Andrews, A. E., Biraud, S. C., Dlugokencky, E. J., Eluszkiewicz, J., Fischer, M. L., Janssens-Maenhout, G., Miller, B. R., Miller, J. B., Montzka, S. A., Nehrkorn, T., and Sweeney, C.: Anthropogenic emissions of methane in the United States, P. Natl. Acad. Sci. USA, 110, 20018–20022, https://doi.org/10.1073/pnas.1314392110, 2013. a
Miller, S. M., Worthy, D. E. J., Michalak, A. M., Wofsy, S. C., Kort, E. A., Havice, T. C., Andrews, A. E., Dlugokencky, E. J., Kaplan, J. O., Levi, P. J., Tian, H., and Zhang, B.: Observational constraints on the distribution, seasonality, and environmental predictors of North American boreal methane emissions, Global Biogeochem. Cycles, 28, 146–160, https://doi.org/10.1002/2013GB004580, 2014. a
Miller, S. M., Miller, C. E., Commane, R., Chang, R. Y.-W., Dinardo, S. J., Henderson, J. M., Karion, A., Lindaas, J., Melton, J. R., Miller, J. B., Sweeney, C., Wofsy, S. C., and Michalak, A. M.: A multiyear estimate of methane fluxes in Alaska from CARVE atmospheric observations, Global Biogeochem. Cycles, 30, 1441–1453, https://doi.org/10.1002/2016GB005419, 2016. a
Miller, S. M., Michalak, A. M., Yadav, V., and Tadić, J. M.: Characterizing biospheric carbon balance using CO2 observations from the OCO-2 satellite, Atmos. Chem. Phys., 18, 6785–6799, https://doi.org/10.5194/acp-18-6785-2018, 2018. a
Miller, S. M., Saibaba, A. K., Trudeau, M. E., Andrews, A. E., Nehrkorn, T., and Mountain, M. E.: Geostatistical inverse modeling with large atmospheric data: data files for a case study from OCO-2, Zenodo [data set], https://doi.org/10.5281/zenodo.11549507, 2024. a
Miller, S. M., Saibaba, A. K., Trudeau, M. E., Mountain, M. E., and Andrews, A. E.: Geostatistical inverse modeling with very large datasets: an example from the Orbiting Carbon Observatory 2 (OCO-2) satellite, Geosci. Model Dev., 13, 1771–1785, https://doi.org/10.5194/gmd-13-1771-2020, 2020a. a, b, c, d, e
Nakamura, G. and Potthast, R.: Inverse Modeling, 2053-2563, IOP Publishing, ISBN 978-0-7503-1218-9, https://doi.org/10.1088/978-0-7503-1218-9, 2015. a
Nehrkorn, T., Eluszkiewicz, J., Wofsy, S., Lin, J., Gerbig, C., Longo, M., and Freitas, S.: Coupled weather research and forecasting–stochastic time-inverted Lagrangian transport (WRF–STILT) model, Meteorol. Atmos. Phys., 107, 51–64, https://doi.org/10.1007/s00703-010-0068-x, 2010. a
Piironen, J. and Vehtari, A.: Sparsity information and regularization in the horseshoe and other shrinkage priors, Electron. J. Statist., 11, 5018–5051, https://doi.org/10.1214/17-EJS1337SI, 2017. a
Randazzo, N. A., Michalak, A. M., Miller, C. E., Miller, S. M., Shiga, Y. P., and Fang, Y.: Higher Autumn Temperatures Lead to Contrasting CO2 Flux Responses in Boreal Forests Versus Tundra and Shrubland, Geophys. Res. Lett., 48, e2021GL093843, https://doi.org/10.1029/2021GL093843, 2021. a, b, c
Rodríguez, P. and Wohlberg, B.: An Efficient Algorithm for Sparse Representations with ℓp Data Fidelity Term, in: Proceedings of 4th IEEE Andean Technical Conference (ANDESCON), 15 October 2008, Cusco, Perú, 2008. a
Saibaba, A. K. and Kitanidis, P. K.: Fast computation of uncertainty quantification measures in the geostatistical approach to solve inverse problems, Adv. Water Resour., 82, 124–138, https://doi.org/10.1016/j.advwatres.2015.04.012, 2015. a
Saunois, M., Stavert, A. R., Poulter, B., Bousquet, P., Canadell, J. G., Jackson, R. B., Raymond, P. A., Dlugokencky, E. J., Houweling, S., Patra, P. K., Ciais, P., Arora, V. K., Bastviken, D., Bergamaschi, P., Blake, D. R., Brailsford, G., Bruhwiler, L., Carlson, K. M., Carrol, M., Castaldi, S., Chandra, N., Crevoisier, C., Crill, P. M., Covey, K., Curry, C. L., Etiope, G., Frankenberg, C., Gedney, N., Hegglin, M. I., Höglund-Isaksson, L., Hugelius, G., Ishizawa, M., Ito, A., Janssens-Maenhout, G., Jensen, K. M., Joos, F., Kleinen, T., Krummel, P. B., Langenfelds, R. L., Laruelle, G. G., Liu, L., Machida, T., Maksyutov, S., McDonald, K. C., McNorton, J., Miller, P. A., Melton, J. R., Morino, I., Müller, J., Murguia-Flores, F., Naik, V., Niwa, Y., Noce, S., O'Doherty, S., Parker, R. J., Peng, C., Peng, S., Peters, G. P., Prigent, C., Prinn, R., Ramonet, M., Regnier, P., Riley, W. J., Rosentreter, J. A., Segers, A., Simpson, I. J., Shi, H., Smith, S. J., Steele, L. P., Thornton, B. F., Tian, H., Tohjima, Y., Tubiello, F. N., Tsuruta, A., Viovy, N., Voulgarakis, A., Weber, T. S., van Weele, M., van der Werf, G. R., Weiss, R. F., Worthy, D., Wunch, D., Yin, Y., Yoshida, Y., Zhang, W., Zhang, Z., Zhao, Y., Zheng, B., Zhu, Q., Zhu, Q., and Zhuang, Q.: The Global Methane Budget 2000–2017, Earth Syst. Sci. Data, 12, 1561–1623, https://doi.org/10.5194/essd-12-1561-2020, 2020. a
Schwarz, G.: Estimating the Dimension of a Model, Ann. Stat., 6, 461–464, https://doi.org/10.1214/aos/1176344136, 1978. a
Shiga, Y. P., Michalak, A. M., Fang, Y., Schaefer, K., Andrews, A. E., Huntzinger, D. H., Schwalm, C. R., Thoning, K., and Wei, Y.: Forests dominate the interannual variability of the North American carbon sink, Environ. Res. Lett., 13, 084015, https://doi.org/10.1088/1748-9326/aad505, 2018a. a, b
Shiga, Y. P., Tadić, J. M., Qiu, X., Yadav, V., Andrews, A. E., Berry, J. A., and Michalak, A. M.: Atmospheric CO2 Observations Reveal Strong Correlation Between Regional Net Biospheric Carbon Uptake and Solar-Induced Chlorophyll Fluorescence, Geophys. Res. Lett., 45, 1122–1132, https://doi.org/10.1002/2017GL076630, 2018b. a, b
Wright, S. J., Nowak, R. D., and Figueiredo, M. A. T.: Sparse reconstruction by separable approximation, in: 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 3373–3376, https://doi.org/10.1109/ICASSP.2008.4518374, 2008. a
Yadav, V., Mueller, K. L., and Michalak, A. M.: A backward elimination discrete optimization algorithm for model selection in spatio-temporal regression models, Environ. Model. Softw., 42, 88–98, https://doi.org/10.1016/j.envsoft.2012.12.009, 2013. a
Yadav, V., Michalak, A. M., Ray, J., and Shiga, Y. P.: A statistical approach for isolating fossil fuel emissions in atmospheric inverse problems, J. Geophys. Res.-Atmos., 121, 12–490, 2016. a
Zhang, M., Berry, J. A., Shiga, Y. P., Doughty, R. B., Madani, N., Li, X., Xiao, J., Sun, Y., Lei, R., and Miller, S. M.: Solar-induced fluorescence helps constrain global patterns in net biosphere exchange, as estimated using atmospheric CO2 observations, J. Geophys. Res.-Biogeo., 128, e2023JG007703, https://doi.org/10.1029/2023JG007703, 2023. a, b, c
Zucchini, W.: An Introduction to Model Selection, J. Math. Psychol., 44, 41–61, https://doi.org/10.1006/jmps.1999.1276, 2000. a
Short summary
Making an informed decision about what prior information to incorporate or discard in an inverse model is important yet very challenging, as it is often not straightforward to distinguish between informative and non-informative variables. In this study, we develop a new approach for incorporating prior information in an inverse model using predictor variables, while simultaneously selecting the relevant predictor variables for the estimation of the unknown quantity of interest.
Making an informed decision about what prior information to incorporate or discard in an inverse...