The CT2026 documentation is best viewed in PDF format as opposed to the web version seen here.

Contents

Chapter 1
Introduction

The goal of the CarbonTracker program is to produce quantitative estimates of atmospheric carbon uptake and release at the Earth’s surface that are consistent with observed patterns of CO₂ in the atmosphere. CarbonTracker is an inverse model of atmospheric CO₂, which means that it attempts to match atmospheric CO₂ measurements by adjusting inputs and removals of carbon dioxide at the Earth’s surface until they best agree with CO₂ measurements and atmospheric transport.

CarbonTracker is updated on an approximately-annual basis. The current release, CT2026, provides results from 2000 through the end of 2025. A “near-real” time model product, CT-NRT, extends these results after the most recent CarbonTracker release. Available model versions are listed at https://gml.noaa.gov/ccgg/carbontracker/version.php.

1.1 A tool for science, and for policy

CarbonTracker is made possible by the long-term monitoring of atmospheric CO₂ conducted by many academic and governmental programs around the world (see Section 5). These data help improve our understanding of how the land and ocean are responding to Earth’s changing climate. The uptake and release of CO₂ by these ecosystems is changing due to chemical and physical responses to increased atmospheric CO₂ concentrations, to human management of lands and oceans, and to changes in temperature, precipitation, and winds.

CarbonTracker is a completely open product. All results, including graphics and tabular data, may be freely used without restriction, although we do request the favor of appropriate acknowledgment (see Section 1.4 and https://gml.noaa.gov/ccgg/carbontracker/citation.php).

The unrestricted access to all CarbonTracker results means that anyone can scrutinize our work, suggest improvements, and profit from our efforts. We hope this scrutiny will help guide further development of our methods, and improve our ability to monitor, diagnose, and possibly predict the behavior of the global carbon cycle. We encourage collaborations focused on use of the CarbonTracker model as a tool for scientific analysis. Please contact us if you would like to get involved and collaborate with us.

CarbonTracker also can be relevant for helping to inform carbon policy. Its ability to accurately quantify natural and anthropogenic emissions and uptake at regional scales is currently limited by a sparse observational network. With enough observations however, CarbonTracker and systems like it will be able to monitor regional emissions, including those from fossil fuel use. This will provide an independent check on emissions accounting, including estimates of fossil fuel use based on economic inventories. It can thus provide feedback to policies aimed at limiting greenhouse gas emissions. This independent evaluation of the effectiveness of carbon policy is the bottom line in any mitigation strategy. It has the added advantage of being a constraint provided by the atmosphere itself, where CO₂ levels matter most.

1.2 The role of other atmospheric species in constraining the atmospheric carbon budget

Many laboratories making high accuracy CO₂ observations also make many other measurements of the same air, typically other greenhouse gases such as methane (CH₄), nitrous oxide (N₂O), sulfur hexafluoride (SF₆), as well as carbon monoxide (CO) and isotopic ratios of CO₂ and CH₄. These measurements are usually reported as mole fractions, for reasons explained here.

These trace gases are relevant for the study of climate change and interesting in their own right, but the additional measurements can also help in identifying sources and sinks of carbon or in understanding carbon cycle processes. For this reason, many air samples are now analyzed for a suite of halocompounds and hydrocarbons. Several of these species can be useful for monitoring air quality, but they can also help with better source apportionment of the greenhouse gases. In addition, the estimation of the source strengths of a number of pollutants could be greatly improved if we were able to quantify fossil fuel CO₂ emissions from air measurements for specified regions.

The best tracer for quantifying the component of atmospheric CO₂ that has been recently added to an air mass through the burning of fossil fuels is the carbon-14 (¹⁴C) content of CO₂. Cosmic rays produce ¹⁴C, a radioactive form of carbon, in the higher regions of the atmosphere. It is present in the atmosphere and oceans and in all living organisms and their remains, but coal, oil, and natural gas contain no ¹⁴C because it has long decayed away. Currently, ¹⁴CO₂ measurements are made on only a small subset of the air samples because of higher analysis costs. None of these other data and their relationships have been used directly in this release of CarbonTracker. We expect them to be incorporated incrementally at later stages.

CarbonTracker is a NOAA contribution to the North American Carbon Program.

1.3 Updates

CarbonTracker is updated about once per year to include new data and model improvements. CT2026 provides results from 2000 through 2025. Previous versions of CarbonTracker and our CT-NRT (CarbonTracker Near-Real Time) releases are available at the CarbonTracker website.

Important revisions of our methods for CT2026 include the following:

• Extension through the end of 2025,

• Revision of fossil fuel emissions,

• New land and wildfire priors,

• Revised air-sea gas exchange including two new 𝑝CO₂ prior models,

• A new Kalman filter time-propagation model, and

• Physical parallelization of the analysis period.

1.4 Citation and usage policy

1.4.1 Usage Policy

CarbonTracker is an open product of NOAA’s Global Monitoring Laboratory (GML) using data from the international greenhouse gas observational network. Results, including figures and tabular material found on the CarbonTracker website may be used for non-commercial purposes without restriction. We kindly ask you to acknowledge, cite, and/or reference CarbonTracker as described below.

1.4.2 Citing our results

• We ask that scientific work that relies heavily on CarbonTracker products is discussed with us before publication, to ensure proper representation of our work and co-authorship if appropriate.

• Please cite as Jacobson et al. (2026).

• The DOI for CT2026 and all its associated products and results is http://dx.doi.org/10.15138/V4W1-2085.

• Please use “CT2026” as the shorthand to refer to our product, not “CT”. This identifies both the product and the release version. It is vital to identify the version of the product you are using.

• Note that the product is called “CarbonTracker” without a space character, not “Carbon Tracker”.

• Please include our suggested acknowledgment text in your acknowledgments section.

• Boilerplate model description text provided upon request.

Example …we compare our results to NOAA’s CarbonTracker, version CT2026 (Jacobson et al., 2026). In this work, CT2026 is …

Acknowledgments CarbonTracker CT2026 results provided by NOAA GML, Boulder, Colorado, USA from the website at http://carbontracker.noaa.gov.

Reference Andrew R. Jacobson, Kenneth N. Schuldt, John B. Miller, Ashley Pera, Aleya Kaushik, Arlyn Andrews, Sourish Basu, Joaquin Triñanes, Peter Landschützer, John Mund, Brad Weir, Lesley Ott, Tuula Aalto, Hermanni Aaltonen, James Brice Abshire, Ken Aikin, Grant Allen, Marcos Andrade, Francesco Apadula, Sabrina Arnold, Bianca Baier, Peter Bakwin, Jakub Bartyzel, Gilles Bentz, Peter Bergamaschi, Andreas Beyersdorf, Tobias Biermann, Sebastien C. Biraud, Pierre-Eric Blanc, Harald Boenisch, David Bowling, Gordon Brailsford, Willi A. Brand, Dominik Brunner, Thao Paul V. Bui, Benoit Burban, Lukas Bäni, Francescopiero Calzolari, Cecilia S. Chang, Gao Chen, Huilin Chen, Lukasz Chmura, Jason M. St. Clair, Shane Clark, Sites Climadat, Julian Della Coletta, Aurelie Colomb, Roisin Commane, Lino Condori, Franz Conen, Sébastien Conil, Cédric Couret, Paolo Cristofanelli, Emilio Cuevas, Roger Curcoll, Bruce Daube, Kenneth J. Davis, Martine De Mazière, Rodrigo A. F. de Souza, Stephan De Wekker, Jonathan M. Dean-Day, Marc Delmotte, Tatiana Di Iorio, Alcide Giorgio di Sarra, Russell Dickerson, Elizabeth DiGangi, Joshua P. DiGangi, Michael Elsasser, Lukas Emmenegger, Shuangxi Fang, Marc L. Fischer, Grant Forster, James France, Arnoud Frumau, Marta Fuente-Lastra, Michal Galkowski, Luciana V. Gatti, Torsten Gehrlein, Christoph Gerbig, Francois Gheusi, Emanuel Gloor, Daisuke Goto, Tim Griffis, Samuel Hammer, Thomas F. Hanisco, Chad Hanson, Shigeru Hashimoto, László Haszpra, Juha Hatakka, Martin Heimann, Michal Heliasz, Daniela Heltai, Stephan Henne, Arjan Hensen, Christian Hermans, Ove Hermansen, Jack Higgs, Eric Hintsa, Antje Hoheisel, Jutta Holst, Laura T. Iraci, Viktor Ivakhov, Daniel A. Jaffe, Lilian Joly, Armin Jordan, Warren Joubert, Hui-Yun Kang, Anna Karion, Stephan Randolph Kawa, Victor Kazan, Ralph F. Keeling, Ishijima Kentaro, Petri Keronen, Jooil Kim, Jörg Klausen, Tobias Kneuer, Mi-Young Ko, Pasi Kolari, Kateřina Komínková, Eric Kort, Elena Kozlova, Paul Krummel, Dagmar Kubistin, Susan S. Kulawik, Nicolas Kumps, Casper Labuschagne, David H.Y. Lam, Xin Lan, Ray L. Langenfelds, Andrea Lanza, Eric Larmanou, Olivier Laurent, Thomas Lauvaux, Jost Lavric, Beverly E. Law, Choong-Hoon Lee, John Lee, Irene Lehner, Kari Lehtinen, Reimo Leppert, Ari Leskinen, Markus Leuenberger, W.H. Leung, Ingeborg Levin, Janne Levula, John Lin, Matthias Lindauer, Anders Lindroth, Zoe Loh, Morgan Lopez, Timothy J. Lueker, Ingrid T. Luijkx, Chris René Lunder, Toshinobu Machida, Ivan Mammarella, Giovanni Manca, Alistair Manning, Andrew Manning, Michal V. Marek, Per Marklund, Josette E. Marrero, Damien Martin, Melissa Yang Martin, Giordane A. Martins, Hidekazu Matsueda, Anna McAuliffe, Kathryn McKain, Harro Meijer, Frank Meinhardt, Lynne Merchant, Jean-Marc Metzger, N. Mihalopoulos, Natasha L. Miles, Charles E. Miller, Logan Mitchell, Meelis Mölder, Jennifer Müller-Williams, Vanessa Monteiro, Stephen Montzka, Heiko Moossen, Caisa Moreno, Eric Morgan, Josep-Anton Morgui, Shinji Morimoto, Hitoshi Mukai, J. William Munger, David Munro, Mathew Mutuku, Cathrine Lund Myhre, Shin-Ichiro Nakaoka, Jaroslaw Necki, Tim Newberger, Sally Newman, Sylvia Nichol, Euan Nisbet, Yosuke Niwa, David Murithi Njiru, Steffen Manfred Noe, Yukihiro Nojiri, Florian Obersteiner, Simon O’Doherty, Bill Paplawsky, Caroline L. Parworth, Jeff Peischl, Olli Peltola, Wouter Peters, Carole Philippon, Salvatore Piacentino, Jean-Marc Pichon, Penelope Pickers, Steve Piper, Joseph Pitt, Christian Plass-Dülmer, Stephen Matthew Platt, Steve Prinzivalli, Michel Ramonet, Ramon Ramos, Xinrong Ren, Enrique Reyes-Sanchez, Scott J. Richardson, Louis-Jeremy Rigouleau, Haris Riris, Pedro P. Rivas, Michael Rothe, Yves-Alain Roulet, Thomas Ryerson, Ju-Mee Ryoo, Maryann Sargent, Motoki Sasakawa, Bert Scheeren, Martina Schmidt, Tanja Schuck, Marcus Schumacher, Jennifer Seibel, Thomas Seifert, Mahesh Kumar Sha, Paul Shepson, Daegeun Shin, Michael Shook, Christopher D. Sloop, Dan Smale, Gerard Spain, Ann Stavert, David Steger, Martin Steinbacher, Britton Stephens, Colm Sweeney, Lise Lotte Sørensen, Risto Taipale, Shinya Takatsuji, Pieter Tans, Yukio Terao, Kirk Thoning, Helder Timas, Margaret Torn, Pamela Trisolino, Kjetil Tørseth, Jocelyn Turnbull, Pim van den Bulk, Alex Vermeulen, Brian Viner, Gabriela Vitkova, Stephen Walker, Andrew Watson, Ray Weiss, Dietmar Weyrauch, Steven C. Wofsy, Sonja Wolter, Justin Worsey, Doug Worthy, Irène Xueref-Remy, Emma L. Yates, Dickon Young, Camille Yver-Kwok, Sönke Zaehle, Andreas Zahn, Christoph Zellweger, Miroslaw Zimnoch. CarbonTracker CT2026, 2026.DOI: 10.25925/hqp0-rk68

Acknowledgment text “CarbonTracker CT2026 results provided by NOAA GML, Boulder, Colorado, USA from the website at http://carbontracker.noaa.gov.”

Suggested Website Citation “CarbonTracker CT2026 http://carbontracker.noaa.gov”

Chapter 2
Model description

CarbonTracker is designed to estimate surface sources and sinks of CO₂ that are consistent with observations of atmospheric CO₂ mole fractions. There are four major components to this effort:

1.

Observations are the measurement constraint that we attempt to meet. We assimilate about 3.5 million CO₂ mole fraction measurements collected by international partners between 2000 and 2025, from surface sites, towers, aircraft, and ships. These are discussed in Chapter 5.

2.

Atmospheric transport provides the connection between surface fluxes and the measured mole fractions of CO₂. We use the TM5 chemical transport model to take surface fluxes and propagate their signals to measurement sites using reanalysis winds. This model is described in Chapter 4.

3.

Prior fluxes are provided by biogeochemical models of surface CO₂ exchange with the atmosphere. If these models and the atmospheric transport we use were perfect, the resulting simulated observations would be in agreement with measured values. However, the match to available observations is not good, suggesting that real fluxes are different from these prior fluxes. CarbonTracker seeks to find the modifications to prior fluxes to yield better agreement with measurements. The collection of prior flux models is discussed in Chapter 3.

We perform two inversions with independent sets of priors, and the final CT2026 fluxes are the mean of those two inversions. The two inversions are coded as “p7” and “p8” and the priors used in them are listed in Table 2.1.

4.

Assimilation is the statistical machinery of finding the optimal fluxes to agree with observations. The unknowns we seek are scaling factors multiplying the prior model CO₂ exchange with the atmosphere for each week over discrete regions. The process of finding the best scaling factors is known as “inverse” modeling. The estimation technique we employ is an ensemble Kalman smoother, as described in Chapter 6.

The inversion process takes prior fluxes which are not consistent with changes in atmospheric CO₂ mole fraction measurements, and scales them regionally and temporally to meet the observational constraint.

The CT2026 inversion process finds a deeper land sink than that estimated by either of the two prior land models (Table 2.2). There is a large disparity in imposed fire fluxes, a difference of 1.2 Pg C yr⁻¹ in the 2001-2025 mean, with the p8 (MiCASA) variant simulating average annual fire emissions of 3.3 Pg C yr⁻¹, compared to the smaller p7 (SiB4/GFED4.1s) emissions of 2.1 Pg C yr⁻¹. Since the observational constraint imposed by the inversion process requires that the sum of global fluxes meets the measured growth in atmospheric CO₂, the p8 inversion must find a correspondingly deeper sink in its optimized NEE and ocean fluxes compared to p7. Indeed, we find that in the long-term mean, the sum of NEE plus ocean optimized fluxes for the p8 inversion is -7.7 Pg C yr⁻¹, and that for p7 is just -6.6 Pg C yr⁻¹.

CarbonTracker results can be explored at the CT2026 website, where there are analysis pages on fluxes and CO₂ measurements.

Chapter 3
Prior models

CarbonTracker CT2026 is a full reanalysis of the 2000-2025 period using new fossil fuel emissions, new air-sea CO₂ exchange, and new terrestrial biosphere priors. In an attempt to quantify the impact of prior model choice on our final results, we conducted two independent inversions with different sets of prior models. These two inversions were coded as “p7” and “p8”. The prior models used for each of these inversions, and the sections of this documents where each is described, are listed in Table 2.1.

3.1 Fossil fuel module

Human beings first influenced the carbon cycle through land-use change. Early humans used fire to control animals and later cleared forests for agriculture. Over the last two centuries, following the industrial and technical revolutions and continuing global population increase, fossil fuel combustion has become the largest anthropogenic source of CO₂. Coal, oil and natural gas combustion are the most common energy sources in both developed and developing countries. Global cement production is also significant, contributing about 5% of total fossil CO₂ emissions. Important sectors of the economy—power generation, transportation, residential & commercial building heating, and industrial processes—rely on fossil fuels. The continued growth of fossil fuel combustion has led to a steady increase of global CO₂ emissions to the atmosphere (Figure 3.1). According to Boden et al. (2017), global emissions of CO₂ from fossil fuel burning, cement manufacturing, and flaring reached 5 billion metric tons of carbon per year (Pg C yr⁻¹) in the decade of the 1970s. Updated emissions products indicate that global total emissions exceeded 10 Pg C yr⁻¹ for the first time in 2018. One petagram of carbon, Pg C, is equal to 10¹⁵ grams of carbon, or one billion metric tons of carbon. To convert to mass of CO₂ emitted, one would multiply by the factor , representing the molecular weight of CO₂ compared to the atomic weight of carbon.

U.S. input of CO₂ to the atmosphere from fossil fuel burning in 2025 was 1.4 Pg C, representing 13% of the global total. North American emissions remained nearly constant from 2000-2018, and decreased slightly during the 2020 COVID-19 pandemic year. On the other hand, emissions from developing economies such as the People’s Republic of China have been increasing. Emissions from China in 2025 were 3.3 Pg C yr⁻¹, representing 30% of the global total.

In almost all global and regional carbon flux estimation systems, including CarbonTracker, fossil fuel CO₂ emissions are not optimized. Instead, these emissions are imposed and are not subject to revision by the inverse modeling framework. Global mass balance requires that any errors in fossil fuel emissions be compensated by opposing errors in land and ocean CO₂ exchange. Thus it is vital that fossil fuel CO₂ emissions are prescribed accurately, so that flux estimates for the land biosphere and oceans are robust. The fossil fuel emissions source data we use are available on an annually-integrated global and national basis. This aggregate information needs to be gridded before being incorporated into CarbonTracker. The major uncertainty in this process is distributing the national-annual emissions spatially across a nation and temporally into hourly contributions. In CT2026, we use two emissions products, called the “Miller” and “OCO-2” emissions datasets.

3.1.1 The “Miller” emissions dataset

Global and National Totals

The Miller fossil fuel emission inventory is derived from independent global total and spatially-resolved inventories (Pera et al., 2026). Annual global total fossil fuel CO₂ emissions are based on the Appalachian Energy Center’s “CDIAC at AppState” project (https://rieee.appstate.edu/projects-programs/cdiac/; Erb and Marland, 2026), which is an effort to update the original annual global and country fossil fuel-CO₂ emissions estimates from the DOE’s Carbon Dioxide Information and Analysis Center (CDIAC) (Boden et al., 2017). The CDIAC at AppState emissions estimates used in CT2026 extend through 2022.

Spatial Distribution

Miller fossil-fuel CO₂ fluxes are spatially distributed in two steps: First, the coarse-scale country totals through 2022 from CDIAC at AppState are mapped onto a 1^◦ × 1^◦ grid according to the spatial patterns from the EDGAR 2025 GHG release (Crippa et al., 2025). The spatial pattern varies by year up until the end of the EDGAR product in 2024. After this, the 2024 spatial pattern is held constant. Note that while EDGAR provides annual emissions estimates at 1^◦ × 1^◦ resolution, their totals do not agree with those from CDIAC at AppState. Thus, only the spatial patterns in EDGAR are used, and the total emissions are rescaled to CDIAC values. The CDIAC country-by-country totals sum to about 95% of the global total emissions; the remaining 5% is mapped to global shipping routes according to EDGAR, which we treat as a proxy for bunker fuel emissions.

Temporal Distribution

For North America between 30 and 60^◦N, the Miller system imposes a seasonal cycle derived from the first and second harmonics (Thoning et al., 1989) of the Blasing et al. (2004) analysis for the United States. The Blasing analysis has ˜10% higher emissions in winter than in summer. This scheme defines a fixed fraction of emissions for each month, so while the shape of the annual cycle is invariant, the amplitude of that cycle scales with the annual total emissions. For Eurasia, a set of seasonal emissions factors from EDGAR distributed by emissions sector is used to define fossil fuel seasonality. As in North America, this seasonality is imposed only from 30-60^◦N. The Eurasian seasonal amplitude is about 25%, significantly larger than that in North America, owing to the absence of a secondary summertime maximum due to air conditioning. See Figure 3.1 for the resulting time series of fossil fuel emissions. In order to avoid discontinuities in the fossil fuel emissions between consecutive years, a spline curve that conserves annual totals (Rasmussen, 1991) is fit to the annual emissions in each 1^◦ × 1^◦ grid cell before the seasonal cycle is imposed.

Whereas early CarbonTracker releases used monthly-constant fossil fuel emissions, starting with CT2015 we introduced the use of temporal scaling factors to simulate day-of-week and diurnal variability for those emissions. These “Temporal Improvements for Modeling Emissions by Scaling” (TIMES) scaling factors, introduced by Nassar et al. (2013), are again applied to the Miller monthly emissions estimates for CT2026. The scaling factors consist of seven day-of-week global scaling factor maps, and 24 hourly global scaling factor maps to represent the diurnal cycle. For use in TM5, the hourly scaling factors were aggregated to three-hourly factors to accommodate the time step of the model.

Extrapolation

The full CDIAC at AppState dataset is only available through 2022 at time of running. A prior estimate of the fluxes through April of 2026 is required to optimize fluxes through the end of 2025, to accommodate our 12-week assimilation window.

For 2023 and 2024 the fractional increases of per-country, sectoral emissions are taken from The Energy Institute (formerly British Petroleum) Statistical Review of World Energy (Energy Institute, 2025) (for coal, oil, gas, and flaring) and the USGS NMIC Cement Mineral Commodity Summaries (for cement emissions). For example, to calculate 2023 coal emissions for France, the EI ratio of 2023 to 2022 coal consumption for France is used to scale 2022 CDIAC emissions, which are then used to rescale the EDGAR spatial patterns. Only the largest producing countries are included in the EI and USGS datasets, so regional or world-average ratios are used for extrapolation of other countries.

For 2025 and the beginning of 2026, global fractional increases are assumed (+2.5% per year for oil and gas, +1% per year for coal and flaring). The final months, February through April 2026, are further scaled by year-on-year ratios from the Carbon Monitor near-real-time estimates (Liu et al., 2020). No fuel-type data is available from Carbon Monitor, so the same year-on-year fractional changes are applied to all fuel types.

3.1.2 The “OCO-2” emissions dataset

The OCO-2 fossil fuel emissions (Basu and Nassar, 2026) were constructed primarily to be used for the OCO-2 Model Intercomparison Project (MIP). We use version 2026.2 of this OCO-2 MIP product.

For 2000–2023, these emission are based on ODIAC 2024 (Tomohiro Oda, 2015), which in turn uses BP’s energy use statistics for 2022 and 2023. ODIAC monthly emissions have been disaggregated to hourly using the TIMES emission factors for day of week and time of day (Nassar et al., 2013). For 2024 onwards, ODIAC’s 2023 emissions were scaled by the ratio of that month to 2023 emissions reported by Carbon Monitor, downloaded on April 24, 2026 from https://carbonmonitor.org/. ODIAC does not have sectoral decomposition to the degree provided by Carbon Monitor, so total ODIAC emissions for each region were scaled by the total emission change between 2023 and each extended year reported by Carbon Monitor. This means that power, ground transport, etc., have not been separately scaled.

Carbon Monitor data are daily, but ODIAC emissions are monthly. Therefore, Carbon Monitor data have been aggregated to monthly totals before deriving scaling factors between 2023 and the extended years. Carbon Monitor reports international aviation emissions by country of origin, while ODIAC reports aviation emissions on a grid. Since there is no way to derive the points of emission for Carbon Monitor aviation emissions, all Carbon Monitor international aviation was aggregated to create a single number for each month, then that number was used to scale ODIAC’s bunker fuel for each month in 2024 and 2025.

CarbonTracker also requires fossil emissions for the first four months of 2026. However, the OCO-2 v2026.2 product only gives estimates through the end of February 2026. To extrapolate to the needed March and April days in 2026, we computed the 2026–2025 difference for the available days (in January and February). The average of this difference was computed, and then added to the corresponding March and April days of 2025 to make emissions in 2026.

3.1.3 Fossil fuel emissions datasets comparisons

Both the Miller and OCO-2 fossil fuel emissions datasets are characterized by an overall increase over the CarbonTracker analysis period (Figure 3.2d). In 2000, global emissions were about 6.7 Pg C yr⁻¹, and by 2025 they have risen to almost 11 Pg C yr⁻¹. Over this period, the OCO-2 emissions are systematically larger by about 0.1 Pg C yr⁻¹. Both emissions datasets manifest a similar dip in 2020 owing to reduced industrial and general transportation activity during the COVID-19 pandemic.

The annual cycle of fossil emissions is strikingly different between these two datasets. In general, the Miller emissions have a regular seasonal cycle throughout the record with a peak-to-peak amplitude larger than the OCO-2 ones. However, in the years after 2020, the ODIAC emissions on which the OCO-2 emissions are based have not only a greater seasonality, but also a marked mid-year peak in emissions. This difference in ODIAC seasonality exists in the original data as distributed at 1^◦ x 1^◦, and is an artifact of how different sectoral emissions are extrapolated after the end of the Erb and Marland (2026) dataset (Tom Oda, private communication, 2026).

While the spatial distribution of long-term emissions as shown in Figures 3.2a and 3.2b is quite similar with emissions concentrated in industrialized countries and the most populous areas, the difference map (Figure 3.2c) shows that the OCO-2 dataset generally predicts more emissions over North America, Europe, and China compared to the Miller emissions. These differences in emissions propagate through the CarbonTracker inversion system to cause differences in inferred land and ocean fluxes, although it is difficult to identify specific effects of the fossil emissions differences.

3.1.4 Uncertainties

Marland (2008) attached an uncertainty of about 5% (95% confidence interval; approximately 2-𝜎) to the global total fossil fuel source. Estimates by Andres et al. (2014) put a larger uncertainty of 8.4% (2-𝜎) on the CDIAC global total. Uncertainties for individual regions of the world, and for sub-annual time periods are likely to be larger. Additional uncertainties are introduced when the emissions are distributed in space and time. In the Miller dataset, the overall Eurasian seasonality is based on scaling factors derived only from Western Europe and thus highly uncertain, but most likely a better representation than assuming no emission seasonality at all. Similarly, the use of the CDIAC monthly emission dataset for modeling seasonality introduces additional uncertainty in ODIAC. The additional uncertainty for the global total in the monthly CDIAC emission, which is solely due to the method for estimating seasonality, is reported as 6.4% (Andres et al., 2011). As mentioned earlier, fossil fuel emissions are not optimized in the current CarbonTracker system, similar to nearly all carbon data analysis systems. Spatial and temporal atmospheric CO₂ gradients arise from terrestrial biosphere and fossil-fuel sources. These gradients, which are interpreted by CarbonTracker, are difficult to attribute to one or the other cause. This is because atmospheric sampling sites have historically been established in locations remote from biospheric and anthropogenic sources, especially in the temperate Northern Hemisphere. Given that surface CO₂ flux due to biospheric activity and oceanic exchange is much more uncertain compared to fossil fuel emissions, CarbonTracker, like most current carbon dioxide data assimilation systems, does not attempt to optimize fossil fuel emissions. That is, the contribution of CO₂ from fossil fuel burning to observed CO₂ mole fractions is considered known. As detailed above, however, in CarbonTracker an effort is made to account for some aspects of fossil fuel uncertainty by using two different fossil fuel estimates. From a technical point of view, extra land biosphere prior flux uncertainty is included in the system to represent the random errors in fossil fuel emissions. Eventually, fossil fuel emissions could be optimized within CarbonTracker, especially with the addition of ¹⁴CO₂ observations as constraints (Basu et al., 2016, 2020).

3.2 Terrestrial biosphere module

The biospheric component of the terrestrial carbon cycle consists of all the carbon stored in ‘biomass’ around us. This includes trees, shrubs, grasses, carbon within soils, dead wood, and leaf litter. Such reservoirs of carbon exchange CO₂ with the atmosphere. This exchange includes plants taking up CO₂ during their growing season, via photosynthesis. Most of this carbon is released back to the atmosphere throughout the year through the process of respiration. Respiration is the conversion of organic carbon back to inorganic CO₂ by plants, animals, and microbes. It includes both the decay of dead wood and litter (heterotrophic respiration), and the metabolic respiration of living plants (autotrophic respiration).

Plants can also return carbon to the atmosphere when they burn, as described in Section 3.3. Even though the yearly sum of uptake and release of carbon amounts to a relatively small number, a few petagrams (one Pg=10¹⁵ g of carbon per year), the flow of carbon each way is as large as 120 Pg C each year. These flows are each affected differently by changes in temperature, water availability, and other factors.

The net result of these land biosphere flows needs to be monitored because of its significant impact on atmospheric CO₂ levels. Due to the relative complexity of the terrestrial carbon cycle, we need a good physical description—a model—of these flows of carbon. This need derives in part from the fact that atmospheric measurements of CO₂ see only the relatively small net sum of the much larger two-way streams, or gross fluxes. Information on what the biospheric fluxes are doing in each season, and in every location on Earth, is derived from specialized land biosphere models, and fed into our system as a first guess, to be refined by our assimilation procedure.

In CT2026, we use the MiCASA and SiB4 terrestrial biosphere models to simulate net ecosystem exchange (NEE), which is the sum of photosynthetic uptake of atmospheric CO₂, and the return of CO₂ to the atmosphere through respiration.

In addition to simulating NEE, each of these models is also coupled to a fire model. Fire models calculate the amount of carbon released to the atmosphere via wildfire and other non-fossil-fuel combustion. As it turns out, both systems use fire models based on the Global Fire Emissions Database (van der Werf et al., 2004, and Section 3.3). As described below, MiCASA uses a modified version of GFED3, and SiB4 imposes its fire emissions directly from the GFED4.1s product.

3.2.1 MiCASA model

First-guess terrestrial biosphere fluxes for CT2026 are provided by the NASA Más informada Carnegie-Ames-Stanford-Approach (MiCASA) v1 model. This model is based on the CASA model introduced by Potter et al. (1993), and provides monthly net primary production (fixation of atmospheric CO₂ via photosynthesis less autotrophic respiration) and heterotrophic respiration at 0.1^◦ x 0.1^◦ lateral resolution. For use in CarbonTracker, these data are spatially averaged to 1^◦ x 1^◦ and temporally downscaled as described in Section 3.2.2. The MiCASA product is documented at https://acdisc.gsfc.nasa.gov/data/CMS/MICASA_FLUX_D.1/doc/MiCASA_README.pdf and is available for download at https://portal.nccs.nasa.gov/datashare/gmao/geos_carb/MiCASA/v1/.

We use the standard v1 product when it exists and the near-real-time vNRT stream for the period that v1 has not yet reached. MiCASA begins in 2001. For 2000 we use the climatology of NPP and heterotrophic respiration computed from the 2001–2025 record. This is also how we handle MiCASA fire emissions in 2000 (Section 3.3.2).

Note that the NASA MiCASA team produces temporally-downscaled GPP, heterotrophic respiration, and fires with 3-hourly resolution. This is done using MERRA-2 meteorology and a scheme similar to Olsen and Randerson (2004). We do not use this downscaled product, in part because the MERRA-2 meteorology is different from the ECMWF meteorology, and in part because the spatial resolution of the MERRA-2 meteorology is different from our 1^◦ × 1^◦ flux grid. Please see Section 3.2.2 below about our temporal downscaling scheme.

The MiCASA team provides an atmospheric correction term computed following the methods described in Weir et al. (2021). This is intended to be added to the native MiCASA flux components to create a terrestrial prior with a sink much closer to that required by atmospheric growth rates. One condition of Bayesian methods is that the prior be unbiased, and this correction term is intended to meet this condition for the MiCASA product. CarbonTracker’s state vector is in scaling factor space instead of flux space, and the condition of having unbiased priors is primarily met by using projected scaling factors. CarbonTracker was in fact designed to correct terrestrial biosphere models with an insufficient land sink. As a result, we do not use this atmospheric correction term.

CASA models directly simulate monthly-mean Net Primary Production (NPP) and heteotrophic respiration (𝑅_𝐻 ) for each terrestrial grid cell being simulated. NPP is the difference in photosynthetic carbon uptake (Gross Primary Production, GPP) and the carbon release by the same plants due to “maintenance respiration”, which is also called autotrophic respiration, 𝑅_𝐴. The carbon uptake represented by NPP and carbon release represented by 𝑅_𝐻 can be differenced to provide Net Ecosystem Exchange (NEE) of CO₂. Throughout this discussion, we use the convention that fluxes carry algebraic signs and we adopt the “atmospheric perspective” for those signs. Thus carbon uptake by the terrestrial biosphere is a negative flux to the atmosphere, and release of CO₂ back to the atmosphere is a positive flux. This means that we represent all respiration fluxes as positive and GPP as negative, so NEE = NPP + 𝑅_𝐻 . This stands in contrast to convention in the terrestrial carbon community, where all fluxes are generally non-negative.

3.2.2 Temporal downscaling

Use of monthly-mean terrestrial fluxes to simulate atmospheric CO₂ is not sufficient to resolve the variability observed at measurement sites. Instead, higher-frequency variations, including the diurnal cycle and effects of passing weather systems must be imposed on the MiCASA monthly fluxes. Following the logic laid out by Olsen and Randerson (2004), we transform the MiCASA-supplied monthly-mean NPP and 𝑅_𝐻 fluxes into GPP and total ecosystem respiration, 𝑅_𝐸 = 𝑅_𝐴 + 𝑅_𝐻 .

To estimate sub-monthly variations, including diurnal and synoptic variability, the Olsen and Randerson (2004) strategy is to model GPP as a linear function of incoming surface solar radiation and total ecosystem respiration as a function of near-surface temperature.

The fundamental assumption needed to apply this scheme is that we can resolve MiCASA-simulated NPP into GPP and 𝑅_𝐴. We apply the assumption that GPP is twice NPP, which further implies that 𝑅_𝐴 is the same size as NPP, but of opposite sign:

(3.1)

(3.2)

and

(3.3)

This fixes the ratio of GPP to autotrophic respiration at 2:1 globally. This is the largest structural assumption in the current and Olsen and Randerson (2004) schemes.

We use meteorological fields from the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 reanalysis to supply fields of surface temperature and shortwave radiation. Fluxes are generated at hourly resolution using a simple temperature 𝑄₁₀ relationship for respiration, assuming a global 𝑄₁₀ value of 1.5 applied to 2-meter air temperature, and a linear scaling of photosynthesis with solar radiation. The procedure is very similar, but not identical to the procedure in Olsen and Randerson (2004). Note that the introduction of hourly variability conserves the monthly mean NEE from MiCASA. Instantaneous NEE for each hour is created as:

(3.4)

where

(3.5)

(3.6)

and 𝑄₁₀ is computed as

(3.7)

where 𝑇_2𝑚 is temperature at 2 meters above the land surface in Kelvin, 𝐼 is surface incoming solar radiation, 𝑡 is time in hourly intervals, and 𝑥_mean represents the monthly mean of quantity 𝑥, including the monthly-mean fluxes derived from MiCASA. Whenever incoming shortwave radiation is zero (for example, during polar night), GPP is forced to zero, and the uptake removed from those hours is redistributed onto the cell’s sunlit hours so that the monthly mean is preserved exactly.

Smooth month-to-month variations

While the scheme outlined above imposes realistic diurnal- and synoptic-scale variations on monthly-mean GPP and 𝑅_𝐸 , it still allows for abrupt changes from one month to the next. For CT2026, we add a further processing step designed to remove such unrealistic step changes. We fit smooth curves to the timeseries of monthly GPP and 𝑅_𝐸 using the monotone piecewise cubic Hermite interpolation (Fritsch and Carlson, 1980). These fits are piecewise quadratic curves that reproduce every monthly mean exactly and are continuous across month boundaries. We use a similar scheme to smooth over year-to-year step changes in fossil fuel emissions. The final smoothed GPP is

(3.8)

and the final smoothed ecosystem respiration is

(3.9)

Together, these form the terrestrial NEE imposed as a first-guess flux in CT2026:

(3.10)

3.2.3 SiB4

The Simple Biosphere Model (SiB4; Haynes et al., 2019a,b) is a mechanistic and process-based model that simulates land-atmosphere exchanges of energy, momentum and moisture, as well as the terrestrial carbon cycle over heterogeneous vegetation. SiB4 combines elements from a prognostic phenology model (Stöckli et al., 2011), a crop model Lokupitiya et al. (2016), and a terrestrial carbon pool model (SiB-CASA; Schaefer et al., 2008). To capture vegetation-specific phenology and biological processes, SiB4 uses 19 plant functional types (PFTs): eight tree PFTs (four types further sub-divided by existence in tropical, temperate, and boreal regions), two shrublands, four grasslands, four crops, and a desert/bare ground classification.

SiB4 was run using ERA5 meteorological drivers, which is the same meteorology as our TM5 transport model. Fluxes were natively produced at scales chosen specifically for CarbonTracker. Spatially, they are produced at 1^◦ x 1^◦ and they have hourly resolution from 2000 through the first few months of 2026.

To simulate land cover heterogeneity, SiB4 uses tiles to allow multiple PFTs in a single grid cell. The magnitude of carbon taken up during photosynthesis depends directly on environmental factors and the fraction of absorbed photosynthetically active radiation. Photosynthesis is coupled to the energy budget, transpiration, and Bowen ratio following Collatz et al. (1991, 1992). Uptake from photosynthesis is either respired for maintenance or allocated to a live carbon pool. Once daily, carbon from live carbon pools is distributed to dead carbon pools following a cascading-pool setup. Heterotrophic respiration resulting from the dead carbon pools is modulated by temperature, moisture, and turnover time.

SiB4 has a relatively aggressive net land sink. Its prior 2001–2025 mean global land sink is almost 4Pg C yr⁻¹. It is understood that this SiB4 land sink is mechanistically dominated by CO₂ fertilization in the photosynthesis scheme. The magnitude of this CO₂ fertilization effect can be estimated by comparing two runs of SiB4, one with a realistically-varying atmospheric CO₂ boundary condition and one with a constant CO₂. That comparison, an approximation of the CO₂ fertilization effect in SiB4, yields a 2000–2019 mean difference of 3 Pg C yr⁻¹, and a significant trend of about 0.7 Pg C yr⁻¹ per decade.

Fire in SiB4

SiB4 imposes GFED4.1s fire emissions by removing burned biomass from its carbon pools. It dynamically allocates burning across its carbon pools following a pre-determined, rudimentary sequential burning of PFTs and carbon pools. Within a given 0.5-degree grid cell, any grasslands that are present are burned first. The remaining PFTs are burned in descending order of total above-ground biomass. Burning continues until the total grid cell emissions equal the GFED4.1s total for that given grid box and time step. In this way, global and regional fire totals from SiB4/GFED4.1s are equivalent to those of GFED4.1s, and fire causes a dynamic reduction and restructuring of carbon pools.

TODO need info on diurnal cycle in SiB4/GFED4.1s fires (Mu et al., 2011). Waiting on response from Sourish on code he wrote for Aleya.

3.2.4 Comparison of terrestrial biosphere priors

The record of atmospheric CO₂ calls for a deeper terrestrial biosphere sink than that generally simulated by terrestrial biosphere models. Inverse models generally simulate a larger annual cycle of terrestrial biosphere fluxes, and in particular a deeper boreal summer uptake of carbon dioxide, in the posterior optimized fluxes compared to the prior models. We call upon the atmospheric CO₂ observations to make this change, and in order to handle these prior model differences the ensemble Kalman filter’s prior covariance model has to be appropriately tuned. In short, this prior uncertainty needs to comfortably span differences among the terrestrial biosphere priors, the fossil fuel emissions estimates, and adjustments to fluxes required to bring model predictions into agreement with observations. CT2026 prior covariances have been adjusted compared to prior releases, and details on this adjustment can be found in Section 6.

Due to the inclusion of fires, inter-annual variability in weather and NDVI, and increasing atmospheric CO₂ levels, NEE fluxes for land regions start with an uptake flux even before optimizing the fluxes. Globally-integrated, this first-guess flux is about -3.2 Pg C yr⁻¹, which is increased in magnitude to about -5.3 Pg C yr⁻¹ by the optimization process. Note that negative fluxes represent a sink of atmospheric CO₂.

3.3 Fire module

Vegetation fires are an important part of the carbon cycle and have been so for many millennia. Even before human civilization began to use fires to clear land for agricultural purposes, most ecosystems were subject to natural wildfires that would rejuvenate old forests and bring important minerals to the soils. When fires consume part of the landscape in either controlled or natural burning, carbon dioxide (among many other gases and aerosols) is released in large quantities. Each year, vegetation fires emit around 2-3 Pg C as CO₂ into the atmosphere, mostly in the tropics.

Currently, a large fraction of wildfire is started by humans. This is mostly intentional to clear land for agriculture, or to re-fertilize soils before a new growing season. This important component of the carbon cycle is monitored mostly from space, while sophisticated ‘biomass burning’ models are used to estimate the amount of CO₂ emitted by each fire. Such estimates are then used in CarbonTracker to prescribe the emissions. These emissions are not modified in the optimization (inverse modeling) process.

3.3.1 GFED fire emissions model

The Global Fire Emissions Database (GFED) was introduced by van der Werf et al. (2004). GFED is driven by satellite observations of fire occurrence, and determines emissions based on carbon pool sizes where fires occur, and indicators of combustion completeness. These carbon pools are provided by a terrestrial biosphere model coupled to GFED. Burned mass is converted to CO₂ emissions using pre-determined emissions factors.

3.3.2 The MiCASA GFED v3 variant

MiCASA v1 simulates biomass burning using a successor model to the CASA-GFED3 model of van der Werf et al. (2004). The NASA MiCASA team produces emissions of wildfire and wood fuel combustion using Moderate Resolution Imaging Spectroradiometer (MODIS) Normalized Difference Vegetation Index (NDVI) computed from reflectances in product MCD43A4.061, burned area from product MCD64A1.061, and carbon fuel stock in various biomass pools estimated from the CASA biogeochemical model. Fire and fuel emissions are available on a daily basis from 2001-2025. For 2000 we apply the climatology of MiCASA fire emissions, computed from its 2001-2025 mean.

In this GFED variant, burned area is based on MODIS satellite observations of fire counts. These, together with detailed vegetation cover information and a set of vegetation specific scaling factors, allow predictions of burned area when active fire counts from MODIS are available. The relationship between fire counts and burned area is derived, for the specific vegetation types, from a calibration subset of 500m resolution burned area from MODIS in the period 2001-2004.

Once burned area has been estimated globally, emissions of trace gases are calculated using carbon pool stocks from the CASA biosphere model. The seasonally changing vegetation and soil biomass stocks in the CASA model are combusted based on the burned area estimate, and converted to atmospheric trace gases using estimates of fuel loads, combustion completeness, and burning efficiency.

3.3.3 GFED4.1s fire emissions

The GFED4 product (Randerson et al., 2017) is an evolution of the Global Fire Emissions Database version 3 (GFED3) biogeochemical model (Randerson et al., 2012). It was later augmented with estimates of emissions from smaller fires not directly seen by the original satellite observations to form the GFED4.1s product.

The GFED4.1s burned area estimate is documented in Giglio et al. (2013), and includes an experimental estimate of small fires. From 2001 onwards, this combines burned area maps from MODIS product MCD64A1 with active fire data from the Tropical Rainfall Measuring Mission (TRMM) Visible and Infrared Scanner (VIRS) and the Along-Track Scanning Radiometer (ATSR) family of sensors. Before 2001, ATSR and VIRS data alone were used. Burned area from small fires depends on active fire detection from MODIS thermal anomalies as described in Randerson et al. (2012). The burned area estimates were converted to emissions using the GFED3 biogeochemical model (Randerson et al., 2012).

3.3.4 Fire emissions comparison

MiCASA is characterized by a significantly larger global fire emissions of about 3.3 Pg C yr⁻¹ averaged over 2000-2025 compared to those of SiB4/GFED4.1s, at 2.1 Pg C yr⁻¹ (Figure 3.5d). This is in part due to the inclusion of an explicit biofuel-burning component in MiCASA, although this only explains about 0.4 Pg C yr⁻¹ of the difference. The MiCASA also simulates larger non-biofuel fire emissions of around 2.9 Pg C yr⁻¹.

The relatively new GFED5 product (van der Werf et al., 2025) computes emissions based on observations of burned area. This approach yields emissions of CO₂ are significantly greater than those of GFED4.1s. A version of SiB4 using burned area is under development, with the constraint that total burned area in both models is conserved. The fire emissions in this new version of SiB4 will come from the product of burned area, pool biomass, and combustion completeness and mortality factors that are modulated by environmental conditions such as aridity.

The relatively large discrepancy in fire emissions between the fire products used in CT2026 increases overall uncertainty in optimized flux results, especially for non-fire land emissions (NEE). The inversion using MiCASA priors estimates a posterior global land NEE of about -5.7 Pg C yr⁻¹, whereas the inversion using SiB4/GFED4.1s priors finds about -5 Pg C yr⁻¹. The remaining difference ends up being ascribed to global ocean fluxes.

3.4 Oceans module

The oceans play an important role in the Earth’s carbon cycle. They are the largest long-term sink for carbon and have an enormous capacity to store and redistribute CO₂ within the Earth system. Oceanographers estimate that about 48% of the CO₂ from fossil fuel burning has been absorbed by the ocean (Sabine et al., 2004). The global ocean CO₂ sink was 2.9 ± 0.4 Pg C yr⁻¹ during the decade 2014-2023, representing 26% of total CO₂ fossil fuel and land use emissions (Friedlingstein et al., 2024). The dissolution of CO₂ in seawater shifts the balance of the ocean carbonate equilibrium towards a more acidic state with a lower pH. This effect is already measurable (Caldeira and Wickett, 2003), and is expected to become an acute challenge to shell-forming organisms over the coming decades and centuries. Although the oceans as a whole have been a reliable sink of carbon over the past decades, CO₂ is also be released from regions of the ocean depending on local temperatures, biological activity, wind speeds, and ocean circulation. These processes are all considered in CarbonTracker, since they can have significant effects on the ocean sink. Improved estimates of the air-sea exchange of carbon in turn help us to understand variability of both the atmospheric burden of CO₂ and terrestrial carbon exchange.

Carbontracker CT2026 finds that the ocean sink begins in 2000 at about about 1 Pg C yr⁻¹, but by 2025 has exceeded 2 Pg C yr⁻¹ (cf. Figure 3.6b and the CT2026 website). This secular increase is modulated by significant interannual variability.

The spatial distribution of CT2026 air-sea exchange of CO₂ is strong extratropical uptake in both the northern and southern hemispheres. Meanwhile, in agreement with our understanding of the ocean carbon cycle, equatorial upwelling of deep CO₂-rich waters leads to an tropical source of carbon to the atmosphere (Figure 3.6a.) This map also reveals some of the internal workings of CarbonTracker, and its limitations. Region-to-region discontinuities are the result of so-called “flux dipoles”, where available observational constraints are not sufficient to uniquely and independently constrain flux from certain regions. In such situations, neighboring regions’ fluxes will play off against one another. This is indicative of CarbonTracker being able to better constrain their sum than each region individually. More well-behaved results can be seen by plotting the flux from larger ocean regions, as in this plot.

3.4.1 Air-sea CO₂ exchange

Oceanic uptake of CO₂ in CarbonTracker is computed using differences in partial pressure of CO₂ between the atmosphere and the ocean surface. The global distribution of seawater partial pressure of CO₂, denoted 𝑝CO₂, is inferred from analysis of direct measurements of that quantity, followed by an interpolation procedure. The resulting global air-sea partial pressure differences are combined with a gas transfer velocity computed from wind speeds in the atmospheric transport model to compute fluxes of carbon dioxide across the sea surface.

In these gas-exchange computations it is formally correct to consider the fugacity of CO₂ instead of its partial pressure (Dickson et al., 2008). Fugacity can be thought of as an effective partial pressure meant to correct for slightly non-ideal gas behavior of CO₂. The difference between fugacity and partial pressure is very small, about 0.3%, and we neglect this correction in our computations.

In the following sections we first describe the SOM-FFN 𝑝CO₂ and AOML-ET prior models. We then describe the air-sea gas transfer velocity parameterization, compare the two priors, and discuss details of the inversion methodology specific to oceanic exchange of CO₂.

3.4.2 SOM-FFN model

One estimate of surface ocean 𝑝CO₂ for CT2026 is provided by the SOM-FFN product of Landschützer et al. (2013). This is a two-step machine-learning system assimilating gridded monthly seawater 𝑝CO₂ measurements from the Surface Ocean CO₂ Atlas project (SOCAT; Bakker et al., 2016). The method first clusters the global ocean into biogeochemical provinces using a self-organized maps method (Kohonen, 1987). In a second step, it reconstructs the nonlinear relationship between driver variables and 𝑝CO₂ observations using a feed-forward neural network. In this way, available measurements are mapped to a globally-complete 1^◦ x 1^◦ monthly ocean grid (Landschützer et al., 2016).

CT2026 uses the SOM-FFN version produced for the 2025 Global Carbon Budget (Friedlingstein et al., 2026) through the end of 2024, and an extrapolation thereafter. All SOM-FFN versions can be downloaded at NCEI (Jersild et al., 2017).

3.4.3 AOML-Extra Trees model

A second estimate of surface ocean 𝑝CO₂ for CT2026 is provided by the NOAA Atlantic Oceanographic and Meteorological Laboratory - Extremely Randomized Trees (AOML-ET; Wanninkhof et al., 2025) system. This is a machine-learning system that assimilates gridded monthly seawater 𝑝CO₂ measurements from the Surface Ocean CO₂ Atlas project (SOCAT; Bakker et al., 2016). These gridded measurements are mapped to a globally-complete 1^◦ x 1^◦ monthly ocean grid using a supervised regression method (Geurts et al., 2006) relying on implicit relationships between 𝑝CO₂ and the chosen regressors of time, location, sea surface temperature, sea surface salinity, chlorophyll, and mixed-layer depth. It provides a spatially and temporally resolved representation of the partial pressure of CO₂ in surface waters. This product accounts for variability in ocean surface properties, including temperature and biological activity, which influence the solubility and concentration of CO₂ in seawater.

CT2026 uses AOML-ET version v20240425 through the end of 2023, and v20250617 thereafter. AOML-ET products are published at NCEI (Wanninkhof et al., 2024).

3.4.4 Gas-transfer velocity and ocean surface properties

Both priors use CO₂ solubilities and Schmidt numbers computed from World Ocean Atlas 2009 (WOA09) climatological fields of sea surface temperature and sea surface salinity fields (Levitus et al., 2010). Gas transfer velocity in CarbonTracker is parameterized as a quadratic function of wind speed following Wanninkhof (2014). Gas exchange is computed every timestep using wind speeds from the ERA5 reanalysis as represented by the atmospheric transport model.

Air-sea transfer is inhibited by the presence of sea ice, and for this work fluxes are scaled by the daily sea ice fraction in each gridbox provided by the ERA5 data.

3.4.5 Specifics of the inversion methodology related to air-sea CO₂ fluxes

The first-guess fluxes described here are subject to scaling during the CarbonTracker optimization process, in which atmospheric CO₂ mole fraction observations are combined with transport simulated by the atmospheric model to infer flux signals. Prior air-sea fluxes are adjusted within each of the 30 ocean inversion regions. In this process, signals of terrestrial flux in atmospheric CO₂ distribution can be erroneously interpreted as being caused by oceanic fluxes. This flux “aliasing” or “leakage” is evident in some regions as a change in the shape of the seasonal cycle of air-sea flux.

Uncertainty on the prior model is specified as uncertainties on scaling factors multiplying net CO₂ flux in each of the 30 ocean inversion regions. In the absence of a suitable uncertainty estimate from the AOML-ET prior model, we apply an uncertainty computed from the ocean interior inversion of Jacobson et al. (2007). This choice is preliminary and will be revised in the future.

3.4.6 Prior ocean emissions comparison

The overall pattern of average air-sea gas exchange as shown in Figures 3.7a and 3.7b is consistent with our understanding of the ocean’s biogeochemical cycling of CO₂. While the global ocean is characterized by overall uptake of CO₂ in the extratropics, the equatorial zone is believed to be a source of CO₂ to the atmosphere (Takahashi et al., 2002). Differences between the two priors in spatial distribution of long-term uptake are generally less than about ± 10g C m⁻² yr⁻¹ (Figure 3.7c). The generally-red colors in this map indicate that over most of the ocean, AOML-ET predicts a smaller ocean sink compared to the SOM-FFN model.

The overall ocean sink is increasing in response to rising atmospheric CO₂ concentrations (Figure 3.7d). The SOM-FFN model consistently predicts a slightly larger ocean sink than AOML-ET (-2 Pg C yr⁻¹ compared to AOML-ET’s long-term average flux of -1.9 Pg C yr⁻¹). While we would hope that the inversion process would help us to converge on a final result for this ocean uptake, we find that the two inversions actually end up with more discrepancy on the long-term mean ocean sink size (-2 for AOML-ET and -1.6 Pg C yr⁻¹ for SOM-FFN in the 2001-2025 mean global posterior flux). This is due to differences in the land priors between the two inversions (see Section 3.3.4), and the inability of available measurements and our system to uniquely quantify ocean uptake.

Chapter 4
Atmospheric transport

The link between observations of CO₂ in the atmosphere and the exchange of CO₂ at the Earth’s surface is transport in the atmosphere: storm systems, cloud complexes, and weather of all sorts cause winds that transport CO₂ around the world. As a result, local surface CO₂ exchange events like fires, forest growth, and ocean upwelling can have impacts at remote locations. To simulate the winds and the weather, CarbonTracker uses sophisticated numerical models that are driven by the daily weather forecasts from the specialized meteorological centers of the world. Since CO₂ does not decay or react in the lower atmosphere, the influence of emissions and uptake in locations such as North America and Europe are ultimately seen in our measurements even at the South Pole. Getting the transport of CO₂ just right is an enormous challenge, and costs us almost all of the computer resources for CarbonTracker. To represent the atmospheric transport, we use the Transport Model 5 (TM5). This is a community-supported model whose development is shared among many scientific groups with different areas of expertise. TM5 is used for many applications other than CarbonTracker, including forecasting air-quality, studying the dispersion of aerosols in the tropics, tracking biomass burning plumes, and predicting pollution levels that future generations might have to deal with.

4.1 TM5 offline tracer transport model

TM5 is an offline global chemical transport model with two-way nested grids. In this global model, regions for which high-resolution simulations are desired can be nested in the coarser global grid. The advantage to this approach is that transport simulations can be performed with a regional focus without the need for boundary conditions. Further, this approach allows measurements outside the “zoom” domain to constrain regional fluxes in the data assimilation, and ensures that regional estimates are consistent with global constraints. TM5 is based on a predecessor model TM3, with improvements in the advection scheme, vertical diffusion parameterization, and meteorological preprocessing of the wind fields (Krol et al., 2005).

The model is developed and maintained jointly by the Institute for Marine and Atmospheric Research Utrecht (IMAU, The Netherlands), the Joint Research Centre (JRC, Italy), the Royal Netherlands Meteorological Institute (KNMI), the Netherlands Institute for Space Research (SRON), and the NOAA Global Monitoring Laboratory (GML).

In CarbonTracker, TM5 separately simulates advection, deep and shallow convection, and vertical diffusion in both the planetary boundary layer and free troposphere. The carbon dioxide concentrations predicted by CarbonTracker do not feed back onto these predictions of winds.

Prior to use in TM5, ECMWF meteorological data are preprocessed into coarser grids, with attention to retrieving a flow that conserves tracer mass. Like most numerical weather prediction models, advection in the parent ECMWF model is not strictly mass-conserving, so this step is crucial. In CarbonTracker, TM5 is currently run at a global 3^◦ longitude × 2^◦ latitude resolution with a nested regional grid over North America at 1^◦ × 1^◦ resolution (Figure 4.1). TM5 uses a dynamically-variable time step with a maximum length of 60 minutes. This overall timestep is dynamically reduced to maintain numerical stability, generally during times of high wind speeds. The timestep is divided in half and individual advection, diffusion, convection, and chemistry operators are applied symmetrically in each half step. Furthermore, transport operators in nested grids are modeled at shorter timesteps, so processes at the finest scales are conducted at an effective timestep of one-quarter the overall timestep. See Krol et al. (2005) for details.

The winds which drive TM5 come from the ERA5 reanalysis implemented in the European Centre for Medium-Range Weather Forecasts (ECMWF) modeling system (Hersbach et al., 2020). The ERA5 reanalysis uses CY41R2 version of the ECMWF Integrated Forecast System (IFS) model. That model uses a 12-minute time step and a spectral T639 horizontal resolution, which corresponds to approximately 28 km spacing at the equator on a reduced Gaussian grid. This version of the IFS has 137 model layers in the vertical, of which TM5 uses a 34-layer subset. The mean heights for these 34 levels are listed in Table 4.1.

4.2 Improvement in convective transport

Before 2013, TM5 was known to have difficulties representing the global surface distribution of sulfur hexafluoride (SF₆, see Figure 4.2 and Peters et al. (2004)). SF₆ is a nearly inert tracer in the atmosphere, with very small surface and atmospheric sinks and an atmospheric lifetime of more than about 800 years. As a result of this long lifetime, its global budget is very well known from observations alone. SF₆ is thought to be released mainly via leakage from electrical transformers. Since the electrical distribution system is closely tied to fossil fuel consumption, SF₆ is often considered an analog for fossil fuel CO₂ in the atmosphere. It is useful for understanding the rate at which Northern Hemisphere land surfaces are ventilated to the free troposphere, and the rate of interhemispheric exchange in models (Patra et al., 2011).

As a result of more than a decade’s worth of work on understanding the apparently sluggish mixing in TM5 as revealed by SF₆ simulations, a fault in one of the vertical mixing parameterizations of the model was discovered. When it was originally created, TM5 implemented the same planetary boundary layer (PBL) mixing and convection schemes as the parent ECMWF model. Recent comparisons between TM5, the ECMWF parent model, and radiosonde profile data show that the PBL scheme in TM5 performs similarly to that of the parent ECMWF model. The pre-2013 convective scheme, however, did not produce similar results in TM5 as compared to the ECMWF model.

Subsequent to the discovery of this convective transport issue, TM5 was modified to use parent model ERA5 convective fluxes directly. Using the parent model convective fluxes result in a significantly better SF₆ simulations. Simulations with these parent-model convective fluxes are said to use the “convective flux fix”. Simulations with the convective flux fix show significantly improved agreement with SF₆ observations (see Figure 4.2).

When the convective flux fix was instituted in CT2013B, it resulted in the largest realignment of surface CO₂ fluxes in the history of the CarbonTracker program (Schuh et al., 2019). This is a prominent example of the sensitive reliance of atmospheric inversions on accurate atmospheric transport.

Chapter 5
Observations

The observations of atmospheric CO₂ mole fraction made by NOAA GML and partner laboratories are at the heart of CarbonTracker. These measurements inform us on changes in the carbon cycle, whether those changes have regular cycles (such as the annual cycle of growth and decay of leaves and other plant matter), or irregular (such as the release of tons of carbon by wildfire). The results in CarbonTracker depend directly on the quality, location, and frequency of available observations. The level of detail at which we can retrieve information on the carbon cycle increases strongly with the density of the CO₂ observing network.

5.1 The CarbonTracker observational network

Observations simulated by CT2026 are supplied by the GLOBALVIEW+ data product version 11.0 (Schuldt et al., 2026), available at the NOAA GML ObsPack web site. This study uses measurements of air samples collected at 679 sites around the world by 80 laboratories:

• The Pennsylvania State University, Department of Meteorology and Atmospheric Science (PSU)

• NOAA Global Monitoring Laboratory (NOAA)

• Instituto de Pesquisas Energeticas e Nucleares (IPEN)

• Environment and Climate Change Canada (ECCC)

• AVOCET Group @ NASA LaRC (NASA-LaRC)

• National Institute for Environmental Studies (NIES)

• Commonwealth Scientific and Industrial Research Organisation, Environment (CSIRO)

• NASA Ames Research Center (NASA-Ames)

• Chinese Academy of Meteorological Sciences (CMA)

• National Institute for Space Research (INPE)

• Scripps Institution of Oceanography (SIO)

• Scripps Institution of Oceanography CO2 Program (SIO_CO2)

• Max Planck Institute for Biogeochemistry (MPI-BGC)

• Laboratoire des Sciences du Climat et de l’Environnement, LSCE/IPSL, CEA-CNRS-UVSQ, Université Paris-Saclay, Gif-sur-Yvett (LSCE)

• Japan Meteorological Agency (JMA)

• NOAA Chemical Sciences Division (NOAA-CSD)

• National Institute of Water and Atmospheric Research (NIWA)

• Integrated Carbon Portal - RI (ICOS RI)

• ICOS Atmosphere Thematic Centre (ICOS-ATC)

• Norwegian Institute for Air Research (NILU)

• University of Bern, Physics Institute, Climate and Environmental Physics (KUP)

• Atmospheric Chemistry Research Group School of Chemistry University of Bristol (UNIVBRIS)

• Department of Earth and Planetary Sciences, Harvard University (HU)

• Earth Networks, Inc., an AEM company (EN)

• Netherlands Organisation for Applied Scientific Research (TNO)

• California Institute of Technology, Division of Geological and Planetary Science (CALTECH)

• Institute of Atmospheric Sciences and Climate (CNR-ISAC) (CNR-ISAC)

• Meteorological Research Institute (MRI)

• South African Weather Service (SAWS)

• Laboratoire d’Aérologie (LA)

• National University of Ireland - Galway (NUI-Galway)

• University of Exeter, Centre for Environmental Data Analysis (CEDA)

• Institut de Ciencia i Tecnologia Ambientals, Universitat Autonoma de Barcelona (ICTA-UAB)

• Lawrence Berkeley National Laboratory and ARM Climate Research Facility (LBNL-ARM)

• University of Maryland, College Park (UMD)

• NOAA Air Resources Laboratory (NOAA-ARL)

• Deutscher Wetterdienst, Hohenpeißenberg Meteorological Observatory (DWD)

• NASA Goddard Space Flight Center (NASA-GSFC)

• Korea Meteorological Administration, Korea Global Atmosphere Watch Center (KMA)

• Joint Research Unit Ecology of Guianan Forests (EcoFoG)

• University of East Anglia (UEA)

• National Center For Atmospheric Research (NCAR)

• University of Heidelberg, Institut fuer Umweltphysik (UHEI-IUP)

• National Physical Laboratory (NPL)

• Hong Kong Observatory (HKO)

• Lund University - Centre for Environmental and Climate Research (LUND-CEC)

• Hungarian Meteorological Service (HMS)

• Karlsruhe Institute of Technology (IMK-ASF) (KIT/IMK-ASF)

• Institute for Atmospheric and Environmental Sciences, University of Frankfurt (IAU)

• Joint Research Centre (JRC)

• Izana Atmospheric Research Center, Meteorological State Agency of Spain (AEMET)

• Estonian University of Life Sciences (EMU)

• Swiss Federal Laboratories for Materials Science and Technology (EMPA)

• AGH University of Krakow (AGH)

• University of Minnesota (UofMN)

• Global Change Research Institute of the Czech Academy of Sciences (CAS)

• Integrated Carbon Observation System - Flask and Calibration Laboratory (ICOS)

• University of Wisconsin (UofWI)

• National Agency for New Technology, Energy, and Environment (ENEA)

• University of Groningen (RUG), Centre for Isotope Research (CIO) (RUG)

• Groupe de Spectrométrie Moléculaire et Atmosphérique (GSMA)

• Kenya Meteorological Department (KMD)

• Royal Holloway University London (RHUL)

• Oregon State University (OSU)

• Laboratory for Atmospheres, Environments, Space Observations (LATMOS) (LATMOS)

• Finnish Meteorological Institute (FMI)

• Ricerca sul Sistema Energetico (RSE)

• Royal Belgian Institute for Space Aeronomy (BIRA-IASB)

• Savannah River National Laboratory (SRNL)

• University of Helsinki (UHELS)

• Aarhus University (AU)

• University of Virginia (UofVA)

• Umweltbundesamt Offenbach/University of Heidelberg, Institut fuer Umweltphysik (UBA/UHEI-IUP)

• Lawrence Berkeley National Laboratory (LBNL)

• Forest Ecology and Management, SLU Umeå (SLU)

• Center for Atmospheric and Oceanic Studies, Tohoku University (TU)

• National Institute of Polar Research (NIPR)

• Main Geophysical Observatory (MGO)

• Utah Atmospheric Trace gas & Air Quality (U-ATAQ)

• Umweltbundesamt Offenbach (UBA-Germany)

The CO₂ measurement data assimilated in CT2026 are freely available for download from the GML ObsPack web portal or from partner websites. The bulk of assimilated measurements come from the GLOBALVIEWplus v11.0 product. Additional observations were gathered from specialized ObsPack products as detailed in Table 5.1.

We also make available an ObsPack containing the simulated values of all measurement data considered by CT2026. This CT2026 ObsPack contains most, but not all, of the measured values. Measured values are only distributed directly when we have permission to do so.

Users are encouraged to review the usage requirements for these data products, and to contact the measurement laboratories directly for details about the observations.

With the advent of GLOBALVIEW+ in 2015, data are now presented to CarbonTracker with a higher temporal frequency than in past observational products. At sites with quasi-continuous monitoring, CT2026 assimilates hourly average CO₂ concentrations. In the past, a single daily assimilation value was constructed at these sites, generally a four-hour average during well-mixed background conditions. At continental sites, this four-hour period was generally from local noon to 4pm; at many mountain sites background conditions are met at nighttime when upslope winds are uncommon. Using GLOBALVIEW+, CarbonTracker can now assimilate each hourly average during these background conditions independently. For many sites, all available hourly averages throughout the day are assimilated. Details vary by dataset, but can be checked at the interactive data plotting page.

Note that all of these observations are calibrated against the same world CO₂ standard (WMO-X2019).

Starting with GLOBALVIEW+, we generally use the recommendations of data providers as to which observations are appropriate for assimilation. Such observations are identified by a variable in the ObsPack distribution, obs_flag. Only observations with obs_flag = 1 are identified for assimilation by data providers. We modify the designation of assimilation data for Environment and Climate Change Canada quasi-continuous sampling sites. For these data, obs_flag is set to 1 by the data provider for times when they represent the daily minimum CO₂ concentration. This is generally later in the day than our standard scheme of local noon-4pm used to represent times of well-mixed PBLs. For these datasets, we have changed obs_flag to indicate assimilation only for the local noon-4pm time period. These selected observations are further filtered based on the CCG curve fitting routine of Thoning et al. (1989). This filter fits a smooth curve to the selected observations, and measurements more than 3 standard deviations away from this curve are excluded from assimilation.

At mountain-top sites (e.g. MLO, NWR, and SPL), it is usually nighttime hours that are selected for assimilation, as these tend to be the most stable time period. Nighttime hours also avoid periods of upslope flows that contain local vegetative and/or anthropogenic influence.

We assimilate CO₂ measurements from NOAA light aircraft profiling time series, from intakes at multiple levels on NOAA tall towers, and from extensive shipboard and Siberian tower measurements collected by our partners at NIES. These datasets can be explored at the interactive data plotting page.

We apply a further selection criterion during the assimilation to exclude non-marine boundary layer (MBL) observations that are very poorly forecasted in our framework. We use the so-called model-data mismatch in this process, which is the random error ascribed to each observation to account for measurement errors as well as modeling errors of that observation. We interpret an observed-minus-forecasted mole fraction that exceeds 3 times the prescribed model-data mismatch as an indicator that our modeling framework fails. This can happen for instance when an air sample is representative of local exchange not captured well by our 1^◦ × 1^◦ fluxes, when local meteorological conditions are not captured by our offline transport fields, but also when large-scale CO₂ exchange is suddenly changed (e.g. fires, pests, droughts) to an extent that can not be accommodated by our flux modules. This last situation would imply an important change in the carbon cycle and has to be recognized by the researchers when analyzing the results. In accordance with the 3-sigma rejection criterion, about 0.2% of the observations are discarded through this mechanism in our assimilation.

5.2 Adaptive model-data mismatch

The statistical optimization method we use to constrain surface CO₂ fluxes requires that each assimilation constraint is assigned a “model-data mismatch” (MDM) error value. This is meant to express the statistics of simulated-minus-observed CO₂ observations we could expect if CarbonTracker were using perfect surface fluxes. Such deviations arise from many sources, including random noise in the measurement system, in situ variability that we do not expect to resolve in our model, and faults with the atmospheric transport model. Generally, transport and inverse model faults are the dominant terms in MDM values. The MDM is one of two major “tuning knobs” used to adjust the performance of our ensemble Kalman filter. The other is also an error quantity, meant to represent the expected error on our first-guess fluxes. Discussion of this prior covariance error can be found in Section 6.3.1.

Prior to CT2015, CarbonTracker used a single MDM value for each assimilation dataset. The NOAA continuous observations at the 396m level of the WLEF tower in northern Wisconsin, for example, were assigned a MDM of 3.0 ppm, meaning that the residuals between model-forecasted measurements and the actual observed concentrations are expected to be unbiased (i.e., have a mean of zero) and have a standard deviation of 3 ppm. In practice, however, we have found that it is far easier to simulate wintertime observations than those during summer. This is mainly due to higher ambient variability of CO₂ in the summer.

Starting with CT2016, we began to use an empirical scheme to assign MDM values, exploiting statistics of model performance from independently-configured preliminary inversions. The posterior residuals for each dataset are classified into relevant bins, and then statistics of model performance are analyzed within each of those bins. For every dataset, these bins include equally-spaced intervals of one-tenth of a year. For analyzers collecting data throughout the day, we also classify the measurements into 4-hour intervals of local time. For aircraft datasets, we further classify measurements into vertical levels of 1000m thickness (0-1000 m ASL, 1000-2000 m ASL, etc.). For each of these bins, bias and random error are combined to form total deviation from observed values as a root-mean square error (RMSE). The assigned MDM is set to a constant fraction of this total RMSE. This scaling is meant to force the assimilation scheme to extract as much information as possible from available observations. We use two different scaling factors to convert RMSE to MDM, depending on whether the preliminary inversions actually assimilated the measurements in the relevant bin, or merely simulated those measurements. For measurements assimilated by the preliminary inversions, the MDM is 0.95 ∗ RMSE. For measurements not assimilated in the preliminary inversions, the MDM is 0.85 ∗ RMSE.

The adaptive MDM scheme performs well in terms of average 𝜒², which in an optimally-tuned system should be close to 1.0 for each dataset (see Table B.1). Notably, the seasonal variations of MDM successfully compensate for the higher ambient variability of CO₂ at continental sites during the growing season. It is, however, an iterative process, requiring that we conduct a previous inversion. For various reasons, this previous inversion performed before CT2026 differs in significant aspects from the actual CT2026 inversions. These differences have led to MDM values which are slightly too large and thus average 𝜒² values which are generally smaller than the target of 1.0 (in some cases, as low as 0.2 or 0.3). The next iteration of CarbonTracker will be able to use the more recent CT2026 inversions to refine the adaptive MDM scheme.

Duplicate observations are identified as those within 50 minutes temporally, 10m vertically, and 0.05 degrees of latitude and longitude laterally (nominally, about 5km). The MDM for such observations is inflated by , where 𝑛 is the number of duplicates.

Chapter 6
Ensemble data assimilation

Data assimilation is the process by which a model simulation is adjusted to agree with observations. Model simulations may drift off from reality for a number of reasons. Some models are highly nonlinear, and depend sensitively on knowing the system state with high accuracy. Weather models fall into this category, and as a result reliable forecast systems depend on having a constant stream of meteorological data to correct their simulations. In contrast, models like CarbonTracker need data assimilation not because the controlling dynamics are nonlinear, but because those dynamics are not well known. CarbonTracker uses approximate or estimated rules about the evolution of surface CO₂ fluxes, then corrects these approximate projections using observational constraints. The resulting optimal surface flux estimates can then be used to better understand the functioning of the carbon cycle.

Data assimilation is usually a cyclical process, in which estimates get refined over time as more observations become available. Mathematically, data assimilation can be performed using a wide variety of techniques, including variational and ensemble methods. Assimilation systems involving simulations of the global atmosphere are often implemented on highly parallel supercomputers in order to distribute the workload among many computational cores. CarbonTracker is an example of such a model because it relies heavily on estimates of global atmospheric transport.

CarbonTracker model predictions are limited by the relatively simple representations of CO₂ surface exchange used to predict land biosphere and ocean fluxes and emissions from fossil fuel combustion and wildfires. As described in the following section, we use data assimilation techniques to modify these surface fluxes so that the resulting atmospheric distribution of CO₂ agrees optimally with measurements. We do this by estimating a set of spatially- and temporally-varying scaling factors that multiply first-guess predictions from prior flux models. Data assimilation allows us to determine optimal values for these scaling factors.

6.1 Parameterization of unknowns

CO₂ fluxes 𝐹(𝑥,𝑦,𝑡) in CarbonTracker are parameterized according to

(6.1)

where 𝐹land, 𝐹ocean, 𝐹FF, and 𝐹bio are prior flux model predictions for land biosphere, ocean, fossil fuel and wildfire emissions respectively, and 1 + 𝜆 represents a set of unknown multiplicative scaling factors applied to the fluxes, to be estimated in the assimilation. These scaling factors are the final product of our assimilation and together with the prior flux models determine CarbonTracker optimized fluxes. Note that no scaling factors are applied to the fossil fuel and fire modules. The fossil fuel and wildfire fluxes are relatively well-known from prior flux models compared to highly-uncertain land biosphere and ocean fluxes, and as a result we impose those emissions without modification in our model.

6.1.1 Optimization regions

The scaling factors 1 + 𝜆 are estimated independently for each week and optimization region. They are assumed to be constant over this time period and spatial domain. Each scaling factor is associated with a particular region of the globe, as in the Transcom inversion study (Gurney et al., 2002). Currently the geographic distribution of these optimization regions is fixed. The choice of regions is a strong a priori design decision determining the reliability of the resulting fluxes. In particular, the scale of optimization regions is chosen to minimize “aggregation errors” (Kaminski et al., 2001), while limiting the set of unknown parameters to a manageable number. Following Jacobson et al. (2007), we have divide the global ocean into 30 basins encompassing large-scale ocean circulation and biogeochemical features. The terrestrial biosphere is divided up according to ecosystem type and geographical domain. Specifically, each of the 11 Transcom land regions is subdivided into a maximum of 19 “ecoregions” according to its Olson et al. (1992) vegetation classification. The set of ecoregions over North America is summarized in Table 6.1 and Figure C.3. Note that there is currently no requirement for ecoregions to be contiguous, and a single scaling factor can be applied to the same vegetation type on both sides of a continent. Further details on ecoregions can be found in Section C.

Theoretically, this approach leads to a total number of 11*19+30=239 optimizable scaling factors for each week, but the actual number of optimization regions is only 156 since some ecosystem types are not represented in every Transcom region. It should be noted also that we have chosen to not optimize scaling factors for ice-covered regions, inland water bodies, and deserts, since the CO₂ flux from these regions is negligible.

It is important to note that even though only one parameter is available to scale, for instance, the flux from coniferous forests in Boreal North America, each 1^◦ × 1^◦ grid box predominantly covered by coniferous forests will have a different optimized flux (1 + 𝜆)𝐹land(𝑥,𝑦,𝑡) depending on local temperature, radiation, and emissions as simulated by the prior flux model.

Ecosystem types are based on the vegetation classification of Olson et al. (1992). Note that we have adjusted the original 29 categories into only 19 regions. This was done mainly to fill the unused categories 16, 17, and 18, and to group the similar categories 23-26 and 29. Table 6.1 shows each vegetation category considered. Percentages indicate the relative area in North America associated with each category.

Each 1^◦ × 1^◦ pixel of our domain was assigned one of the categories above based on the Olson category that was most prevalent in the 0.5^◦ × 0.5^◦ underlying area.

6.1.2 Assimilation window

Measured CO₂ mole fractions are the result of upstream surface fluxes and atmospheric transport, which includes both advective movement and diffusive mixing. Near-field surface fluxes can cause significant changes in CO₂ mole fractions, whereas flux signals from further upstream become spread out and diluted. Generally speaking, the longer in the past a flux event occurred, the smaller its impact will be on a given sample of air (although it will be spread out through a larger volume of the atmosphere). Thus we choose an “assimilation window” that represents how far back in time we expect to be able to pinpoint a given flux signal from available measurements. A good discussion of this topic can be found in Bruhwiler et al. (2005).

In previous versions of CarbonTracker, the assimilation window was chosen to be five weeks long, meaning that a measurement could cause revisions in surface fluxes only over the 5 weeks leading up to that measurement. In CT2026, we have extended the assimilation window length to 12 weeks. This helps to resolve fluxes in regions of the world with less dense observational coverage (the tropics, Southern Hemisphere, and parts of Asia).

This assimilation window is moved forward on each cycle of our estimation system, so that new weeks are introduced at the “head” of the filter, and the weeks that fall out the “tail” of the filter are finalized. Prior to CT2026, the 5-week assimilation window was moved forward one week at a time. In CT2026, the 12-week assimilation window is moved forward two weeks at a time. Scaling factors 1 + 𝜆 retain their weekly resolution. Each cycle of the inversion system requires running the atmospheric model for a length of time equal to the assimilation window length plus the window step size. For previous CarbonTracker releases, this was 6 weeks per cycle; for CT2026 it is 14 weeks per cycle. The extra computing time required by the longer assimilation window is balanced somewhat by the two-week stepping.

Ensemble size and localization

The ensemble system used to solve for the scalar multiplication factors is similar to that in Peters et al. (2005) and based on the square root ensemble Kalman filter of Whitaker and Hamill (2002). Ensemble statistics are created from 600 randomly-chosen members, each with its own background CO₂ concentration field to represent the time history of that member’s surface fluxes. The ensemble Kalman filter looks for correlations between these random flux perturbations and resulting changes in simulated CO₂ measurements. We might expect that the entire ensemble would agree that increasing the CO₂ flux in a given region results in greater simulated CO₂ at a nearby downwind site. However, because we approximate the flux covariance matrix with a random sample of 600 members, sometimes spurious correlations appear. It is unphysical, for instance, that a measurement at Summit, Greenland could be strongly influenced by surface exchange in the southern Indian Ocean, within the time span of our assimilation window. Any such correlation between the flux ensemble and the measurement in question is likely spurious. Localization is a technique developed for numerical weather prediction in which unphysical correlations are diagnosed and systematically ignored (Houtekamer and Mitchell, 1998). We perform localization for our measurements, but only for certain datasets. Notably, it is not used for datasets judged to represent hemisphere-scale signals, such as those from marine boundary layer sites in remote locations.

Our localization technique is based on the linear correlation coefficient between the 600 parameter deviations and 600 observation deviations for each parameter/observation pair. If the relationship between a parameter deviation and its modeled observational impact is statistically significant, then that relationship is retained. Otherwise, the relationship is assumed to be spurious noise due to the numerical approximation of the covariance matrix by the limited ensemble. We accept relationships that reach 95% significance in a Student’s T-test with a two-tailed probability distribution.

6.2 Physical parallelization

In CT2026 we break our analysis period into segments initialized every three years, which are then run simultaneously. These segments start on 1 January of 2000, 2003, …, 2021, and 2024. Each segment is initialized with an analyzed CO₂ field appropriate to the starting date and the same prior state (cf.  Section 6.3). “Physical parallelization” of this type was introduced for CO₂ analyses by Chevallier (2013). This procedure has reduced the time to produce a CarbonTracker release by about an order of magnitude.

The final CT2026 fluxes and simulated mole fractions are formed by stitching together the parallelized segments. A given segment 𝑛 takes up to a 18 months to equilibrate in mole fraction and flux space to the same state as the previous segment 𝑛 − 1, which has integrated for three additional years. Chevallier (2013) evaluated segment overlap in a variational framework and found that a three-month overlap was appropriate for that system. With the ensemble Kalman filter, we can evaluate the segment overlap not only in simulated CO₂ mole fraction space, but also in flux and flux uncertainty space. We find in simulation experiments and in the current operational inversions that an overlap of 18 months produces statistically consistent segment states. Thus the CT2026 results are composed of first-segment data from January 2000 to mid-July 2004, at which point results from the second segment (initialized at January 1, 2003) are imposed. This process is continued to stitch together results from all nine segments.

6.3 Dynamical model

With CT2026 we introduce a new dynamical model, based on a linear time propagation operator, Ψ. Previous versions of CarbonTracker used a more ad hoc dynamical model that was not consistent with the mathematics of the Kalman filter. The time propagation operator is used to estimate the prior state at time 𝑡, denoted {𝜆⁻[𝑡],𝑃_𝜆⁻[𝑡]}, from the posterior state at time 𝑡 − 1, which is written as {𝜆⁺[𝑡 − 1],𝑃_𝜆⁺[𝑡 − 1]}. This is a linear transformation of the state, expressed as

(6.2)

and

(6.3)

where the prior value of the scaling factors for timestep 𝑡 is 1 + 𝜆⁻[𝑡], the posterior at timestep 𝑡 − 1 is 1 + 𝜆⁺[𝑡 − 1], and 𝜖_Ψ is a mean-zero noise process representing uncertainty in this temporal propagation model. The covariance matrix of the 𝜖_Ψ noise process is 𝑃_Ψ.

In practice the mean state is evolved without adding an explicit 𝜖_Ψ, but the ensemble deviations are seeded with random noise drawn from 𝑃_Ψ. This process noise is extremely important in the Kalman filter, since it is responsible for maintaining a minimum amount of error covariance in the ensemble. In effect this keeps freedom, or “wiggle-room”, in the state so that the system can respond to new signals in measurements destined for assimilation. This state freedom prevents premature convergence to a faulty solution. The addition of process noise is a sort of error inflation.

The time propagation scheme chosen for CT2026 is based on modified persistence. In this scheme, scaling factor parameters are assumed to decay back towards unity with a certain smoothing timescale. Mathematically, we express this as:

(6.4)

where 𝜏 is a timescale parameter and Δ𝑡 is the amount of time over which the state is being propagated. We use 𝜏 = 7 days. Ψ is a diagonal matrix, which means that the scaling factors evolve independently from one another.

6.3.1 Structure of master prior covariance

The “master” prior covariance matrix 𝑃₀⁻ is used to initialize the ensemble Kalman filter on its first timestep, and to inject process noise in the time propagation step. It describes the magnitude of the uncertainty on each parameter, plus their correlations. The correlations between the same ecosystem types in different Transcom regions decrease exponentially with distance scale 𝐿 = 2000km, and thus assumes a coupling between the behavior of the same ecosystems in close proximity to one another (such as coniferous forests in Boreal and Temperate North America). Furthermore, all ecosystems within tropical Transcom regions are coupled decreasing exponentially with distance since we do not believe the current observing network can constrain tropical fluxes on sub-continental scales, and want to prevent spurious compensating source/sink pairs (“dipoles”) to occur in the tropics.

While the correlation structure discussed above has remained fixed in all CarbonTracker releases, we have been changing the overall magnitude of the covariance matrix in an attempt to mitigate seasonal biases in our simulated CO₂ fields. Since those biases appear mostly in comparison to measurement data over land, and also because the annual cycle of CO₂ in the atmosphere is dominated by the terrestrial carbon cycle, we experimented by loosening the land prior constraint. As it turns out, these biases were mostly due to our original short assimilation window length (Section 6.1.2) and the convective flux problem discussed in Section 4.2. As a result, for CT2026 we were able to scale back the land prior covariance. “L-curve” analysis (Hansen, 1998) suggested that these covariances could be reduced even from the original levels, and new values are shown in red in the lower panel of Figure 6.1.

6.3.2 Process Noise

As previously discussed, the process noise 𝑃_Ψ is a crucial “tuning knob” in the Kalman filter. While formally it represents uncertainty in the time propagation methodology, in practice it is responsible for maintaining a minimum level of flexibility in the state. In a series of simulation experiments, different versions of the CarbonTracker dynamical model Ψ and 𝑃_Ψ were tested until an optimal version was identified.

In these simulation experiments, synthetic measurement data were generated from a known truth condition. These synthetic observations were then corrupted with random noise drawn from the assumed model-data mismatch (see Section 5.2). Each simulation experiment consisted of a three-year inversion in which these synthetic measurements were assimilated into a CarbonTracker run. These fluxes estimated by these runs were then evaluated against the truth condition. This evaluation consisted both of quantifying the differences between retrieved and true fluxes, and also evaluating whether those differences were spanned by the posterior uncertainties.

The most successful process noise parameterization was found by adding a scaled version of the initial prior covariance matrix 𝑃₀⁻:

(6.5)

6.3.3 Posterior uncertainties in CarbonTracker

In CT2026, our error estimates on optimized fluxes are considerably more realistic as a result of adopting a formally-correct linear time propagation scheme. Notably, they reflect the density of measurement constraints in various regions. Previous CarbonTracker releases were far more aggressive about covariance inflation, which resulted in unrealistically large posterior errors.

CT2026 uncertainties do not resolve errors which are correlated in time. This is due to the limited extent of our assimilation window, in which these temporal error covariances are only modestly resolved. The present assimilation window of 12 weeks, with a two-week stepping, means that only the very shortest temporal correlations would be resolved. However, these short (anti) correlations are quite evident in CT2026 posterior fluxes, and we are exploring methods for including temporal information in CarbonTracker uncertainties.

Chapter 7
Statistical performance of CT2026

7.1 Measurement data

Starting with CT2022, we started to reserve about 5% of available assimilation data for a cross-validation exercise. To the extent possible, withheld measurements were chosen to be independent from other observations. For surface flask observations, which are generally collected on a weekly time basis, all samples are considered independent from one another, so withheld data were selected randomly. Aircraft flasks collected during a profile are considered co-dependent, so entire profiles were randomly selected for withholding. Finally, for in situ analyzers with quasi-continuous sampling (towers, observatories), 24-hour periods were randomly chosen and that entire day’s worth of data were withheld. Shipboard quasi-continuous datasets, which account for more than a quarter of assimilation data for CT2026 were inadvertently excluded from this cross-validation exercise. As a result, about 5% (166,097 measurements out of almost 3.5 million) were withheld.

Each residual from the withheld measurements was divided by its prescribed model-data mismatch (MDM) error, to form a set of normalized residuals. From this sequence we can compute the mean (or reduced) chi-squared statistic 𝜒², which for a perfect set of independent, normally-distributed variates should approach unity, is 1.2. This is quite similar to the same statistic for assimilated data, which is 1.04 (see Table 7.1).

These slightly inflated 𝜒² values are actually as intended. They indicate that the model-data mismatch values used in CarbonTracker are too small. This in turn suggests that the RMSE deflation described is Section 5.2 probably is too agressive, but it also means that the Kalman filtering scheme will attempt to fit measurement data at the expense of retrieving a less-smooth flux solution. This overfitting will be revised in upcoming CarbonTracker releases.

Chapter 8
Resources and References

• Global Fire Emissions Database (GFED) web page

• NASA GFED_CMS CASA project

• Olson ecosystem types

• GFED_CMS web page at NACP

• DOE Energy Information Administration (EIA)

• BP Statistical Review of World Energy

• EDGAR Database

• DMSP satellite nightlight data

• Centre for Air Transport and the Environment (CATE), AERO2k aviation emissions inventory

• The Surface Ocean CO₂ Atlas

• NOAA Pacific Marine Environmental Laboratory

• Ocean Acidification

• GML Carbon Cycle Program

• WMO/GAW Report No. 168, 2006

Bibliography

Appendix A
Full author list

Andrew R. Jacobson^1,2, Kenneth N. Schuldt^1,2, John B. Miller², Ashley Pera^1,2,
Aleya Kaushik^1,2, Arlyn Andrews^2(retired),3, Sourish Basu^4,5, Joaquin Triñanes^6,7,8,
Peter Landschützer⁹, Brad Weir^10,4, Lesley Ott⁴, John Mund^1,2,
Tuula Aalto¹¹, Hermanni Aaltonen¹¹, James Brice Abshire¹², Ken Aikin¹³,
Grant Allen¹⁴, Marcos Andrade¹⁵, Francesco Apadula¹⁶, Sabrina Arnold¹⁷,
Bianca Baier², Peter Bakwin, Jakub Bartyzel¹⁸, Gilles Bentz¹⁹,
Peter Bergamaschi²⁰, Andreas Beyersdorf²¹, Tobias Biermann²², Sebastien C. Biraud²³,
Pierre-Eric Blanc²⁴, Harald Boenisch²⁵, David Bowling²⁶, Gordon Brailsford²⁷,
Willi A. Brand²⁸, Dominik Brunner²⁹, Thao Paul V. Bui³⁰, Benoit Burban³¹,
Lukas Bäni³², Francescopiero Calzolari³³, Cecilia S. Chang³⁰, Gao Chen³⁴,
Huilin Chen³⁵, Lukasz Chmura¹⁸, Jason M. St. Clair¹², Shane Clark³⁶,
Sites Climadat³⁷, Julian Della Coletta³⁸, Aurelie Colomb³⁹, Roisin Commane⁴⁰,
Lino Condori⁴¹, Franz Conen⁴², Sébastien Conil⁴³, Cédric Couret⁴⁴,
Paolo Cristofanelli³³, Emilio Cuevas⁴⁵, Roger Curcoll³⁷, Bruce Daube⁴⁰,
Kenneth J. Davis⁴⁶, Martine De Mazière⁴⁷, Rodrigo A. F. de Souza⁴⁸, Stephan De Wekker⁴⁹,
Jonathan M. Dean-Day³⁰, Marc Delmotte¹⁹, Tatiana Di Iorio⁵⁰, Alcide Giorgio di Sarra⁵⁰,
Russell Dickerson¹⁵, Elizabeth DiGangi⁵¹, Joshua P. DiGangi³⁴, Michael Elsasser⁵²,
Lukas Emmenegger²⁹, Shuangxi Fang⁵³, Marc L. Fischer⁵⁴, Grant Forster^55,56,
James France⁵⁷, Arnoud Frumau⁵⁸, Marta Fuente-Lastra¹⁹, Michal Galkowski¹⁸,
Luciana V. Gatti⁵⁹, Torsten Gehrlein²⁵, Christoph Gerbig²⁸, Francois Gheusi⁶⁰,
Emanuel Gloor⁶¹, Daisuke Goto⁶², Tim Griffis⁶³, Samuel Hammer³⁸,
Thomas F. Hanisco¹², Chad Hanson⁶⁴, Shigeru Hashimoto⁶⁵, László Haszpra⁶⁶,
Juha Hatakka¹¹, Martin Heimann²⁸, Michal Heliasz²², Daniela Heltai¹⁶,
Stephan Henne²⁹, Arjan Hensen⁵⁸, Christian Hermans⁶⁷, Ove Hermansen⁶⁸,
Jack Higgs², Eric Hintsa², Antje Hoheisel³⁸, Jutta Holst⁶⁹,
Laura T. Iraci³⁰, Viktor Ivakhov⁷⁰, Daniel A. Jaffe⁷¹, Lilian Joly⁷²,
Armin Jordan²⁸, Warren Joubert⁷³, Hui-Yun Kang⁷⁴, Anna Karion⁷⁵,
Stephan Randolph Kawa¹², Victor Kazan¹⁹, Ralph F. Keeling³⁶, Ishijima Kentaro⁶⁵,
Petri Keronen⁷⁶, Jooil Kim³⁶, Jörg Klausen⁷⁷, Tobias Kneuer⁷⁸,
Mi-Young Ko⁷⁴, Pasi Kolari⁷⁶, Kateřina Komínková⁷⁹, Eric Kort⁸⁰,
Elena Kozlova⁸¹, Paul Krummel⁸², Dagmar Kubistin⁷⁸, Susan S. Kulawik³⁰,
Nicolas Kumps⁶⁷, Casper Labuschagne⁷³, David H.Y. Lam⁸³, Xin Lan^1,2,
Ray L. Langenfelds⁸², Andrea Lanza¹⁶, Eric Larmanou⁸⁴, Olivier Laurent⁸⁵,
Thomas Lauvaux^72,46, Jost Lavric²⁸, Beverly E. Law⁶⁴, Choong-Hoon Lee⁷⁴,
John Lee⁸⁶, Irene Lehner²², Kari Lehtinen¹¹, Reimo Leppert²⁸,
Ari Leskinen^87,88, Markus Leuenberger³², W.H. Leung⁸³, Ingeborg Levin³⁸,
Janne Levula⁷⁶, John Lin²⁶, Matthias Lindauer⁷⁸, Anders Lindroth⁶⁹,
Zoe Loh⁸², Morgan Lopez¹⁹, Timothy J. Lueker³⁶, Ingrid T. Luijkx^89,90,
Chris René Lunder⁶⁸, Toshinobu Machida⁶⁵, Ivan Mammarella⁹¹, Giovanni Manca²⁰,
Alistair Manning⁹², Andrew Manning⁵⁶, Michal V. Marek⁷⁹, Per Marklund⁸⁴,
Josette E. Marrero³⁰, Damien Martin⁹³, Melissa Yang Martin³⁴, Giordane A. Martins⁹⁴,
Hidekazu Matsueda⁹⁵, Anna McAuliffe^1,2, Kathryn McKain², Harro Meijer³⁵,
Frank Meinhardt⁹⁶, Lynne Merchant³⁶, Jean-Marc Metzger⁴⁷, N. Mihalopoulos⁹⁷,
Natasha L. Miles⁴⁶, Charles E. Miller⁹⁸, Logan Mitchell²⁶, Meelis Mölder⁶⁹,
Jennifer Müller-Williams⁷⁸, Vanessa Monteiro⁴⁶, Stephen Montzka², Heiko Moossen²⁸,
Caisa Moreno, Eric Morgan³⁶, Josep-Anton Morgui³⁷, Shinji Morimoto⁹⁹,
Hitoshi Mukai⁶⁵, J. William Munger⁴⁰, David Munro², Mathew Mutuku¹⁰⁰,
Cathrine Lund Myhre⁶⁸, Shin-Ichiro Nakaoka⁶⁵, Jaroslaw Necki¹⁸, Tim Newberger²,
Sally Newman¹⁰¹, Sylvia Nichol²⁷, Euan Nisbet⁵⁷, Yosuke Niwa⁶⁵,
David Murithi Njiru¹⁰⁰, Steffen Manfred Noe¹⁰², Yukihiro Nojiri⁶⁵, Simon O’Doherty¹⁰³,
Florian Obersteiner²⁵, Simon O’Doherty¹⁰³, Bill Paplawsky³⁶, Caroline L. Parworth³⁰,
Jeff Peischl^1,13, Olli Peltola⁷⁶, Wouter Peters³⁵, Carole Philippon¹⁹,
Salvatore Piacentino⁵⁰, Jean-Marc Pichon³⁹, Penelope Pickers⁵⁶, Steve Piper³⁶,
Joseph Pitt¹⁰³, Christian Plass-Dülmer⁷⁸, Stephen Matthew Platt⁶⁸, Steve Prinzivalli⁵¹,
Michel Ramonet¹⁹, Ramon Ramos⁴⁵, Xinrong Ren¹⁰⁴, Enrique Reyes-Sanchez⁴⁵,
Scott J. Richardson⁴⁶, Louis-Jeremy Rigouleau¹⁹, Haris Riris¹², Pedro P. Rivas⁴⁵,
Michael Rothe²⁸, Yves-Alain Roulet⁷⁷, Thomas Ryerson¹³, Ju-Mee Ryoo³⁰,
Maryann Sargent⁴⁰, Motoki Sasakawa⁶⁵, Bert Scheeren³⁵, Martina Schmidt¹⁹,
Tanja Schuck¹⁰⁵, Marcus Schumacher²⁸, Jennifer Seibel³⁶, Thomas Seifert²⁸,
Mahesh Kumar Sha⁶⁷, Paul Shepson¹⁰⁶, Daegeun Shin⁷⁴, Michael Shook³⁴,
Christopher D. Sloop⁵¹, Dan Smale²⁷, Gerard Spain⁹³, Ann Stavert⁸²,
David Steger²⁹, Martin Steinbacher²⁹, Britton Stephens¹⁰⁷, Colm Sweeney²,
Lise Lotte Sørensen¹⁰⁸, Risto Taipale⁷⁶, Shinya Takatsuji¹⁰⁹, Pieter Tans¹¹⁰,
Yukio Terao⁶⁵, Kirk Thoning², Helder Timas¹¹¹, Margaret Torn⁵⁴,
Pamela Trisolino³³, Kjetil Tørseth⁶⁸, Jocelyn Turnbull^112,1, Pim van den Bulk⁵⁸,
Alex Vermeulen⁶⁹, Brian Viner¹¹³, Gabriela Vitkova⁷⁹, Stephen Walker³⁶,
Andrew Watson⁸¹, Ray Weiss³⁶, Dietmar Weyrauch⁷⁸, Steven C. Wofsy⁴⁰,
Sonja Wolter², Justin Worsey⁸¹, Doug Worthy¹¹⁴, Irène Xueref-Remy¹¹⁵,
Emma L. Yates³⁰, Dickon Young¹⁰³, Camille Yver-Kwok¹⁹, Sönke Zaehle²⁸,
Andreas Zahn²⁵, Christoph Zellweger²⁹ and Miroslaw Zimnoch¹⁸

¹CIRES, University of Colorado, Boulder, Colorado, USA
²NOAA Global Monitoring Laboratory, Boulder, Colorado, USA
³Former Feds and Friends, LLC
⁴Global Modeling and Assimilation Office, NASA Goddard Space Flight Center, Greenbelt, Maryland, USA
⁵Earth System Science Interdisciplinary Center, University of Maryland, College Park, Maryland, USA
⁶Atlantic Oceanographic and Meteorological Laboratory, National Oceanic and Atmospheric Administration, Miami, FL
⁷Rosenstiel School of Marine, Atmospheric and Earth Science, Cooperative Institute for Marine and Atmospheric Studies, University of Miami, Miami, FL
⁸Department of Electronics and Computer Science, Universidadede Santiago de Compostela, Santiago, Spain
⁹Vlaams Instituut voor de Zee, Oostende, België
¹⁰Morgan State University, Baltimore, Maryland, USA
¹¹Finnish Meteorological Institute, Climate System Research, Helsinki, Finland
¹²NASA Goddard Space Flight Center, Greenbelt, Maryland, USA
¹³NOAA Chemical Sciences Laboratory, Boulder, Colorado, USA
¹⁴University of Manchester, Manchester, England
¹⁵Department of Atmospheric and Oceanic Science, University of Maryland, College Park, Maryland, USA
¹⁶Ricerca sul Sistema Energetico– RSE S.p.A., Milano, Italy
¹⁷Deutsches Zentrum für Luft- und Raumfahrt (DLR), Institut für Physik der Atmosphäre, Oberpfaffenhofen, Germany
¹⁸AGH University of Science and Technology, Krakow, Poland
¹⁹Laboratoire des Sciences du Climat et de l’Environnement, LSCE/IPSL, CEA-CNRS-UVSQ, Université Paris-Saclay, Gif-sur-Yvette, France
²⁰European Commission, Joint Research Centre, Ispra, Italy
²¹California State University, San Bernardino, California, USA
²²Lund University, Centre for Environmental and Climate Science, Lund, Sweden
²³ARM Carbon Project, Lawrence Berkeley National Laboratory, Berkeley, California, USA
²⁴Observatory of Universe Sciences Pytheas, Aix-Marseille University, Marseille, France
²⁵Institute for Meteorology and Climate Research (IMK), Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
²⁶Department of Atmospheric Sciences, University of Utah, Salt Lake City, Utah, USA
²⁷National Institute of Water and Atmospheric Research, Wellington, New Zealand
²⁸Max Planck Institute for Biogeochemistry, Jena, Germany
²⁹Empa, Swiss Federal Laboratories for Materials Science and Technology, Laboratory for Air Pollution/Environmental Technology, Dübendorf, Switzerland
³⁰NASA Ames Research Center, Moffett Field, California, USA
³¹Joint Research Unit Ecology of Guianan Forests
³²Climate and Environmental Physics, University of Bern, Bern, Switzerland
³³Institute of Atmospheric Sciences and Climate (CNR-ISAC), Bologna, Italy
³⁴NASA Langley Research Center, Hampton, Virginia, USA
³⁵Centre for Isotope Research, University of Groningen, Groningen, Netherlands
³⁶Scripps Institution of Oceanography, University of California, La Jolla, California, USA
³⁷Institut de Ciencia i Tecnologia Ambientals, Universitat Autonoma de Barcelona, Barcelona, Spain
³⁸Universität Heidelberg, Institut für Umweltphysik, Heidelberg, Germany
³⁹Observatoire de Physique du Globe de Clermont Ferrand, Aubiere, France
⁴⁰Harvard University, School of Engineering and Applied Sciences, Cambridge, Massachusetts, USA
⁴¹Servicio Meteorológico Nacional, Argentina
⁴²University of Basel, Basel, Switzerland
⁴³Agence Nationale pour la Gestion des Déchets Radioactifs, France
⁴⁴Umweltbundesamt, Zugspitze, Germany
⁴⁵Agencia Estatal Meteorologia, Santa Cruz de Tenerife, Spain
⁴⁶The Pennsylvania State University, Department of Meteorology and Atmospheric Science, University Park, Pennsylvania, USA
⁴⁷Observatoire de Physique de l’Atmosphère de la Réunion
⁴⁸Amazonas State University, Manaus, Brazil
⁴⁹University of Virginia, Charlottesville, Virginia, USA
⁵⁰Italian National Agency for New Technologies, Energy and Sustainable Economic Development, UTMEA-TER Earth Observations and Analyses Laboratory, Rome, Italy
⁵¹Earth Networks, Inc., an AEM company, Germantown, Maryland, USA
⁵²Umweltbundesamt, Salzburg, Germany
⁵³Meteorological Observation Centre, Chinese Meteorological Administration, Beijing, China
⁵⁴Lawrence Berkeley National Laboratory, Berkeley, California, USA
⁵⁵National Centre for Atmospheric Sciences, University of East Anglia, Norwich, Norfolk, United Kingdom
⁵⁶Centre for Ocean and Atmospheric Sciences, University of East Anglia, Norfolk, United Kingdom
⁵⁷Royal Holloway, University of London, United Kingdom
⁵⁸Netherlands Organisation for Applied Scientific Research (TNO), Petten, The Netherlands
⁵⁹National Institute for Space Research (INPE), Sao Paulo, Brazil
⁶⁰Observatoire Midi-Pyrénées, Toulouse, France
⁶¹University of Leeds,School of Geography, Leeds, United Kingdom
⁶²National Institute of Polar Research, Tokyo, Japan
⁶³University of Minnesota,Department of Soil, Water, and Climate, St. Paul, Minnesota, USA
⁶⁴Oregon State University, Corvallis, Oregon, USA
⁶⁵National Instiute for Environmental Studies, Tsukuba, Japan
⁶⁶Institute for Nuclear Research, Debrecen, Hungary
⁶⁷Royal Belgian Institute for Space Aeronomy, Brussels, Belgium
⁶⁸NILU, Kjeller, Norway
⁶⁹Lund University, Dept. Phys. Geography and Ecosystem Science, Lund, Sweden
⁷⁰Voeikov Main Geophysical Observatory,Saint Petersburg, Russia
⁷¹University of Washington, Seattle, Washington, USA
⁷²University of Reims Champagne-Ardenne, CNRS, Reims, France
⁷³South African Weather Service, Cape Point, South Africa
⁷⁴Korea Meteorological Administration, Seoul, South Korea
⁷⁵National Institute of Standards and Technology, Gaithersburg, Maryland, USA
⁷⁶University of Helsinki, Helsinki, Finland
⁷⁷Federal Office of Meteorology and Climatology MeteoSwiss, Switzerland
⁷⁸Deutscher Wetterdienst, Hohenpeißenberg Meteorological Observatory, Hohenpeißenberg, Germany
⁷⁹Global Change Research Institute of the Czech Academy of Sciences, Brno, Czech Republic
⁸⁰University of Michigan, Ann Arbor, Michigan, USA
⁸¹University of Exeter, Centre for Environmental Data Analysis, Exeter, Devon, United Kingdom
⁸²Commonwealth Scientific and Industrial Research Organisation, Environment, Aspendale, Victoria, Australia
⁸³Hong Kong Observatory, Hong Kong, China
⁸⁴Svartberget Field Research Station, Swedish University of Agricultural Sciences, Vindeln, Sweden
⁸⁵ICOS Atmospheric Thematic Centre, Gif-sur-Yvette, France
⁸⁶University of Maine, Orono, Maine, USA
⁸⁷University of Eastern Finland, Department of Technical Physics, Kuopio, Finland
⁸⁸Finnish Meteorological Institute, Kuopio, Finland
⁸⁹Wageningen University, Wageningen, Netherlands
⁹⁰ ICOS Carbon Portal, Lund University, Lund, Sweden
⁹¹Institute for Atmospheric and Earth System Research/Physics, Faculty of Sciences, University of Helsinki, Finland
⁹²Met Office Exeter, Devon, United Kingdom
⁹³National University of Ireland, Galway, Ireland
⁹⁴Fundacão Amazônica de Defesa da Atmosfera, Manaus, Brazil
⁹⁵Meteorological Research Institute, Tsukuba, Japan
⁹⁶Umweltbundesamt, Oberried-Hofsgrund, Germany
⁹⁷Environmental and Chemical Processes Laboratory, University of Crete, Crete, Greece
⁹⁸Jet Propulsion Laboratory, California Institute of Technology, Pasadena California, USA
⁹⁹Tohoku University, Sendai, Japan
¹⁰⁰Kenya Meteorological Department, Nairobi, Kenya
¹⁰¹California Institute of Technology, Pasadena, California, USA
¹⁰²Estonian University of Life Sciences, Institute of Forestry and Engineering, Tartu, Estonia
¹⁰³University of Bristol, Bristol, United Kingdom
¹⁰⁴NOAA Air Resources Laboratory, College Park, Maryland, USA
¹⁰⁵Institute for Atmospheric and Environmental Sciences, University of Frankfurt, Frankfurt, Germany
¹⁰⁶Purdue University, West Lafayette, Indiana, USA
¹⁰⁷National Center for Atmospheric Research, Boulder, Colorado, USA
¹⁰⁸Aarhus University, Aarhus Centrum, Denmark
¹⁰⁹Japan Meteorological Agency, Tokyo, Japan
¹¹⁰Institute of Arctic and Alpine Research,University of Colorado, Boulder, Colorado, USA
¹¹¹Instituto Nacional de Meteorologia e Geofisica, Cidade de Espargos, Ilha do Sal, República de Cabo Verde
¹¹²GNS Science,National Isotope Centre, Lower Hutt, New Zealand
¹¹³Savannah River National Laboratory, Aiken, South Carolina, USA
¹¹⁴Environment and Climate Change Canado, Ontario, Canada
¹¹⁵Aix-Marseille University, Marseille, France

Appendix B
Performance by dataset

Table B.1 summarizes the datasets assimilated in CarbonTracker, and the performance of the assimilation scheme for each dataset. These diagnostics are useful for evaluating how well CarbonTracker does in simulating observed CO₂.

Summary of Observational Sites Used in CarbonTracker. The site location is specified by latitude, longitude and elevation in meters above sea level. The number of observations actually assimilated for each dataset is listed in the column “Used”, and the number rejected due to inability to fit the observations is listed in the column “Rej.”. Model-data-mismatch (𝑅) is a value assigned to a given site that is meant to quantify our expected ability to simulate observations there. In this table we report the range of 𝑅values assigned to dataset observations by our “adaptive” model-data mismatch scheme (Section 5.2). These values are principally determined from the limitations of the atmospheric transport model. It is part of the standard deviation used to interpret the difference between a simulation first guess (𝐻𝑥) of an observation and the actual measured value (𝑧). The other component, 𝐻𝑃𝐻T, is a measure of the ability of the ensemble Kalman filter to improve its simulated value for this observation by adjusting fluxes. These elements together form the innovation 𝜒 statistic for the site: 𝜒 =(𝑧− 𝐻𝑥)/ . The innovation 𝜒² reported above is the mean of all squared normalized values for a given site. An average 𝜒² below 1.0 indicates that the 𝐻𝑃𝐻T + 𝑅² values are too large. Conversely, values above 1.0 mean that this standard deviation is underestimated. The bias and SE columns are statistics of the posterior residuals (final modeled values minus measured values). The bias is the mean of these residuals; the SE is the standard error of those residuals.

Appendix C
Ecoregions in CarbonTracker

C.1 What are ecoregions?

Ecoregions are the actual scale on which CarbonTracker performs its optimization over land. Ecoregions are meant to represent large expanses of land within a given continent having similar ecosystem types, and are used to divide continent-scale regions into smaller domains for analysis. The ecosystem types use in CarbonTracker are derived from the Olson et al. (1992) vegetation classification (Table C.1, Figure C.1).

We define an ecoregion as an ecosystem type within a given Transcom land region. There are 19 ecosystem types we extract from the Olson et al. (1992) system, and 11 Transcom land regions (Figure C.2), so there are 11 × 19 = 209 possible ecoregions. However, not all ecosystem types are present in all Transcom regions, and the actual number of land ecoregions ends up being 126.

Note on “Semitundra”: this is a potentially misleading shorthand abbreviation for a collection of ecosystems comprising semi-desert, shrubs, steppe, and polar+alpine tundra. The “Semitundra” zones appearing in northern Africa where one expects to find the Sahara desert are not, of course, tundra environments. They are instead semi-desert zones.

C.2 Why use ecoregions?

A fundamental challenge to atmospheric inversions like CarbonTracker is that there are not enough observations to directly constrain fluxes at all times and in all places. It is therefore necessary to find a way to reduce the number of unknowns being estimated. Strategies to reduce the number of unknowns in problems like this one generally impose information from external sources. In CarbonTracker, we reduce the problem size both by estimating fluxes at the ecoregion scale, and by using a terrestrial biological model to give a first guess flux from the ecoregion. The model is also used to give the spatial and temporal distribution of CO₂ flux within a region and week.

C.3 Ecosystems within Transcom regions

Each Transcom land region (Figure C.2) can contain up to 19 ecoregions.