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 CO₂ at the Earth’s surface until they best agree with those observational constraints. CarbonTracker is updated on a approximately-annual basis. The current release, CT2026, provides results from 2000 through the end of 2024. A “near-real” time model product, CT-NRT, extends these results through 2025 and later. Current model versions are listed on 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 Sec. 7). 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 Sec. 1.5 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.

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 A community effort

CarbonTracker is intended to be a tool for the community, and we welcome feedback and collaboration from anyone interested. Our ability to accurately track carbon with more spatial and temporal detail is fundamentally dependent on our collective ability to make enough measurements to characterize variability present in the atmosphere. For example, estimates suggest that observations from tall communication towers (taller than 200m) can tell us about carbon uptake and emission over a radius of only several hundred kilometers. The map of observation sites (Fig. 7.2) shows how sparse the current network is. One way to join this effort is by contributing measurements to the GLOBALVIEW+ project. Regular air samples collected from the surface, towers or aircraft are needed. It would also be very fruitful to expand use of continuous measurements like the ones now being made on very tall (more than 200m) communications towers. Another way to join this effort is by volunteering flux estimates from your own work, to be run through CarbonTracker and assessed against atmospheric CO₂ measurements. We also 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.

1.3 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.

1.4 Updates

CarbonTracker is updated about once per year to include new data and model improvements. CT2026 provides results from 2000 through 2020. 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 2024,

• Revision of fossil fuel emissions,

• New land and wildfire priors, and

• Revised air-sea gas exchange including a new pCO2 prior model.

1.5 Citation and usage policy

1.5.1 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.

1.5.2 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. [2025]

• 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., 2025]. 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, Arlyn Andrews, John B. Miller, Tomohiro Oda, Sourish Basu, John Mund, Brad Weir, Lesley Ott, Rik Wanninkhof, Joaquin Triñanes, Tuula Aalto, James Brice Abshire, Grant Allen, Marcos Andrade, Francesco Apadula, Sabrina Arnold, Bianca Baier, Jakub Bartyzel, Andreas Beyersdorf, Tobias Biermann, Sebastien C. Biraud, Pierre-Eric Blanc, Harald Boenisch, Gordon Brailsford, Willi A. Brand, Dominik Brunner, Pim van den Bulk, Benoit Burban, Lukas Bäni, Francescopiero Calzolari, Cecilia S. Chang, Gao Chen, Huilin Chen, Lukasz Chmura, Shane Clark, 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, Marc Delmotte, Elizabeth DiGangi, Joshua P. DiGangi, Russell Dickerson, Michael Elsasser, Lukas Emmenegger, Shuangxi Fang, 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, Chad Hanson, László Haszpra, Juha Hatakka, Martin Heimann, Michal Heliasz, Daniela Heltai, Stephan Henne, Arjan Hensen, Christian Hermans, Ove Hermansen, Eric Hintsa, Antje Hoheisel, Jutta Holst, Tatiana Di Iorio, Laura T. Iraci, Viktor Ivakhov, Daniel A. Jaffe, Armin Jordan, Armin Jordan, Warren Joubert, Hui-Yun Kang, Anna Karion, Stephan Randolph Kawa, Victor Kazan, Ralph F. Keeling, Petri Keronen, Jooil Kim, Jörg Klausen, Tobias Kneuer, Mi-Young Ko, Pasi Kolari, Kateřina Komínková, Eric Kort, Elena Kozlova, Paul B. Krummel, Dagmar Kubistin, Nicolas Kumps, Casper Labuschagne, David H.Y. Lam, Xin Lan, Ray L. Langenfelds, Andrea Lanza, Olivier Laurent, Tuomas Laurila, Thomas Lauvaux, Jost Lavric, Beverly E. Law, John Lee, Olivia S.M. Lee, Choong-Hoon 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 M. Loh, Morgan Lopez, Ingrid T. Luijkx, Chris René Lunder, Meelis Mölder, Jennifer Müller-Williams, Toshinobu Machida, Ivan Mammarella, Giovanni Manca, Alistair Manning, Andrew Manning, Michal V. Marek, Damien Martin, Giordane A. Martins, Hidekazu Matsueda, Martine De Mazière, Kathryn McKain, Harro Meijer, Frank Meinhardt, Lynne Merchant, Jean-Marc Metzger, N. Mihalopoulos, Natasha L. Miles, Charles E. Miller, Logan Mitchell, Vanessa Monteiro, Stephen Montzka, Heiko Moossen, Caisa Moreno, Eric Morgan, Josep-Anton Morgui, Shinji Morimoto, J. William Munger, David Munro, Mathew Mutuku, Cathrine Lund Myhre, Jennifer Müller-Williams, Shin-Ichiro Nakaoka, Jaroslaw Necki, Sally Newman, Sylvia Nichol, Euan Nisbet, Yosuke Niwa, David Murithi Njiru, Steffen Manfred Noe, Yukihiro Nojiri, Simon O’Doherty, Florian Obersteiner, Bill Paplawsky, 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, Xinrong Ren, Enrique Reyes-Sanchez, Scott J. Richardson, Haris Riris, Pedro P. Rivas, Yves-Alain Roulet, Maryann Sargent, Alcide Giorgio di Sarra, Motoki Sasakawa, Hinrich Schaefer, Bert Scheeren, Tanja Schuck, Marcus Schumacher, Jennifer Seibel, Thomas Seifert, Mahesh Kumar Sha, Paul Shepson, Daegeun Shin, Michael Shook, Christopher D. Sloop, Dan Smale, Paul D. Smith, Rodrigo A. F. de Souza, Gerard Spain, Martin Steinbacher, Britton Stephens, Colm Sweeney, Lise Lotte Sørensen, Risto Taipale, Shinya Takatsuji, Kirk Thoning, Helder Timas, Margaret Torn, Pamela Trisolino, Jocelyn Turnbull, Alex Vermeulen, Brian Viner, Gabriela Vitkova, Stephen Walker, Andrew Watson, Ray Weiss, Stephan De Wekker, Steven C. Wofsy, Justin Worsey, Doug Worthy, Irène Xueref-Remy, Emma L. Yates, Dickon Young, Camille Yver-Kwok, Sönke Zaehle, Andreas Zahn, Christoph Zellweger, Miroslaw Zimnoch. CarbonTracker CT2025, 2025. DOI: 10.15138/v4w1-2085

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
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 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. 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.

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 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 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/.

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, so the condition of having unbiased priors is not met by using corrected fluxes. Indeed, CarbonTracker was designed to correct terrestrial biosphere models with an insufficient land sink. As a result, we do not use this atmospheric correction term.

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^∘Õ 1^∘ flux grid. Please see Section 2.2 below about our temporal downscaling scheme.

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.

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 CASA monthly fluxes. Following the logic laid out by Olsen and Randerson [2004], we transform the CASA-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 CASA-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):

(2.1)

(2.2)

and

(2.3)

We use meteorological fields from the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 reanalysis to supply temperature and shortwave radiation. Fluxes are generated with 90-minute variability using a simple temperature Q₁₀ relationship for respiration, assuming a global Q₁₀ value of 1.5, 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 90-minute variability conserves the monthly mean NEE from the CASA model. Instantaneous NEE for each 90-minute interval is created as:

(2.4)

where

(2.5)

(2.6)

and Q₁₀ is computed as

(2.7)

where T_2m is temperature at 2 meters above the land surface in Kelvin, I is surface incoming solar radiation, t is time in 90-minute intervals, and x_mean represents the monthly mean of quantity x, including the monthly-mean fluxes derived from the CASA model.

2.2.1 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 monthly GPP and R_E using the piecewise integral quadratic splines (PIQS) of Rasmussen [1991]. These PIQS fits are continuous in the first and second derivatives, and have the property of preserving monthly mean flux. We use a similar scheme to smooth over year-to-year step changes in fossil fuel emissions. The final smoothed GPP is

(2.8)

and the final smoothed ecosystem respiration is

(2.9)

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

(2.10)

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The record of atmospheric CO₂ calls for a deeper terrestrial biosphere sink than that generally simulated by terrestrial biosphere models like MiCASA. Inverse models manifesting such a sink 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 (See Fig. 2.2). 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 8.

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CarbonTracker CT2026 is a full reanalysis of the 2000–2024 period using new fossil fuel emissions, new air-sea CO₂ exchange, and new terrestrial biosphere priors (including fire emissions) from MiCASA v1.

Due to the inclusion of fires, inter-annual variability in weather and NDVI, the fluxes for North America start with a small net flux even before optimizing the fluxes. This first-guess flux ranges from neutral exchange to about XXX Pg C yr⁻¹ of uptake.

Chapter 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 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.

In CT2026 we use MiCASA v1 fire emissions datasets, with daily temporal resolution.

3.1 Global Fire Emissions Database (GFED)

CT2026 uses MiCASA v1 fire emissions to represent biomass burning. This fire model is a successor 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 MODIS NDVI computed from the Terra + Aqua BRDF-adjusted Reflectances Version 6.1 (MCD43A4.061), MODIS Terra + Aqua Version 6.1 Burned Area (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 2000–2024 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.

Chapter 4
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 (Fig. 4.3). 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.

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U.S. input of CO₂ to the atmosphere from fossil fuel burning in 2020 was 1.3 Pg C, representing 13% of the global total. North American emissions remained nearly constant from 2000–2018, and decreased slightly during the 2020 COVID 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 2020 were 2.8 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 a product called the “Miller” emissions datasets.

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.

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4.1 The “Miller” emissions dataset

Global and National Totals

The Miller fossil fuel emission inventory is derived from independent global total and spatially-resolved inventories. 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/), 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 2020.

Spatial Distribution

Miller fossil-fuel CO₂ fluxes are spatially distributed in two steps: First, the coarse-scale country totals through 2020 from CDIAC at AppState are mapped onto a 1^∘ × 1^∘ grid according to the spatial patterns from the EDGAR v8.0 inventories [Commission et al., 2019]. The spatial pattern varies by year up until the end of the EDGAR v8.0 product in 2022. After this, the trends estimated in each cell (pixel) are linearly extrapolated. 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 4.3 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 seasonal emissions in each 1^∘ × 1^∘ grid cell.

Extrapolation

The full CDIAC at AppState and EDGAR dataset are only available from 2000 through 2020 at time of running. A prior estimate of the fluxes through April of 2025 is required to optimize fluxes through the end of 2024, to accommodate our 12-week assimilation window.

For 2021 through the end of 2023 the fractional increases of per-country, sectoral emissions are taken from The Energy Institute (formerly British Petroleum) Statistical Review of World Energy [BP, 2021] (for coal, oil, gas, and flaring) and the USGS NMIC Cement Mineral Commodity Summaries (for cement emissions). For example, to calculate July 2022 coal emissions for France, the EI ratio of July 2022 to July 2020 emissions for France are used to scale July 2020 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 a world-average is used for extrapolation of other regions.

For 2024 and the beginning of 2025, global fractional increases are held constant. No fuel-type data is available from CarbonMonitor, so the same year-on-year fractional changes are applied to all fuel types.

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4.2 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].

Chapter 5
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 relatively steady net carbon sink, CO₂ can also be released from oceans 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.

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The initial release of CarbonTracker (CT2007) used climatological estimates of CO₂ partial pressure in surface waters (pCO₂) from Takahashi et al. [2002,  2009] to compute a first-guess air-sea flux. This air-sea pCO2 disequilibrium was modulated by a surface barometric pressure correction before being multiplied by a gas-transfer coefficient to yield a flux. Starting with CT2007B and continuing through the CT2011_oi release, the air-sea pCO2 disequilibrium was imposed from analysis of ocean inversions [Jacobson et al., 2007, “OIF”] results, with short-term flux variability derived from the atmospheric model wind speeds via the gas transfer coefficient. The barometric pressure correction was removed so that climatological high- and low-pressure cells did not bias the long-term means of the first guess fluxes.

5.1 Air-sea gas exchange

Oceanic uptake of CO₂ in CarbonTracker is computed using differences in partial pressure of CO₂ between the atmosphere and the ocean surface. The 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. 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 0.3neglect this correction in our computations.

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

5.2 AOML-Extra Trees model

Surface ocean pCO2 for CT2026 is provided by the NOAA Atlantic Oceanographic and Meteorological Laboratory - Extremely Randomized Trees Wanninkhof et al. [2025, AOML-ET;] system. This is a machine-learning system that assimilates gridded monthly seawater pCO2 measurements from the Surface Ocean CO₂ Atlas project [Bakker et al., 2016, SOCAT;]. These gridded measurements are mapped to a globally-complete 1^∘ x 1^∘ monthly ocean grid using a supervised classification 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].

5.3 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.

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5.4 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.

Chapter 6
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.

6.1 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 6.1). TM5 uses a dynamically-variable time step with a maximum length of 90 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.

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The winds which drive TM5 come from the ERA5 reanalysis implemented in the European Centre for Medium-Range Weather Forecasts (ECMWF) modeling system. 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. These levels are listed in Table 6.1.

6.2 Convective flux fix

Until recently, TM5 was known to have difficulties representing the global surface distribution of sulfur hexafluoride (SF₆, see Figure 6.2 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 about 1,000 years. Consequently, its global budget is very well known from observations alone. It 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 convective scheme, however, does not produce similar results in TM5 as compared to the ECMWF model.

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In a previous configuration of TM5, the convective entrainment and detrainment mass fluxes of the parent ECMWF model were re-diagnosed within TM5 using other meteorological information. The ECMWF model is used to produce both operational forecasts and the ERA-interim reanalysis, but the convective fluxes are stored for the ERA-interim product only. Thus, using ERA-interim meteorology, a direct comparison is possible. This comparison revealed that the TM5 internal rediagnosis of convective fluxes was faulty. TM5 was subsequently modified to use parent model ERA-interim 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 6.2).

Since the parent-model convective fluxes are only available for the ERA-interim product, CT2026 uses only ERA-interim transport with the convective flux fix. Previous releases of CarbonTracker also used the ECMWF operational model transport, for which parent-model convective fluxes are not available. We believe that TM5 simulations without the parent-model convective fluxes are faulty and should not be included in our product. 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 7
Observations

The observations of atmospheric CO₂ mole fraction made by NOAA GML and partner laboratories are at the heart of CarbonTracker. They inform us on changes in the carbon cycle, whether those changes are regular (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 a 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.

7.1 The CarbonTracker observational network

Observations simulated by CT2026 are supplied by the GLOBALVIEW+ data product versions 9.1 and 10.1 [Schuldt et al., 2023,  2024], available at the NOAA GML ObsPack web site. This study uses measurements of air samples collected at 559 sites around the world by 66 laboratories:

• Penn State University (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)

• CSIRO Oceans and Atmosphere, Climate Science Centre-GASLAB (CSIRO)

• Chinese Academy of Meteorological Sciences (CMA)

• 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-UMR8212 CEA-CNRS-UVSQ (LSCE)

• Japan Meteorological Agency (JMA)

• NOAA Chemical Sciences Division (NOAA-CSD)

• National Institute of Water and Atmospheric Research (NIWA)

• 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)

• Harvard University (HU)

• 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)

• 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)

• Hohenpeissenberg Meteorological Observatory (HPB)

• Earth Networks, Inc. (EN)

• NASA Goddard Space Flight Center (NASA-GSFC)

• National Center For Atmospheric Research (NCAR)

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

• NOAA ESRL Halocarbons and Other Atmospheric Trace Species (NOAA-HATS)

• 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)

• High Altitude Research Stations Jungfraujoch and Gornergrat International Foundation (HFSJG)

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

• University of Science and Technology (AGH) (AGH)

• University of Minnesota (UofMN)

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

• Czechglobe-Global Change Research Institute CAS (CAS)

• University of Wisconsin (UofWI)

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

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

• Oregon State University (OSU)

• Finnish Meteorological Institute (FMI)

• Ricerca sul Sistema Energetico (RSE)

• Commissariat à l’énergie atomique et aux énergies alternatives (CEA)

• Savannah River National Laboratory (SRNL)

• University of Helsinki (UHELS)

• University of Virginia (UofVA)

• Umweltbundesamt, Station Schauinsland (UBA-SCHAU)

• Lawrence Berkeley National Laboratory (LBNL)

• Forest Ecology and Management, SLU Umeå (SLU)

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

• University of East Anglia (UEA)

• Main Geophysical Observatory (MGO)

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

• Umweltbundesamt, Zugspitze GAW Station (UBA/ZUG)

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 GLOBALVIEWplus v9.1 (2023) and from the GLOBALVIEWplus v10.1 product. Additional observations were gathered from specialized ObsPack products as detailed in Table 7.1.

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.

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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.

Data from the Sutro tower (STR) and the Boulder (Erie, Colorado) tower (BAO) are strongly influenced by local urban emissions, which CarbonTracker is unable to resolve. At these two sites, pollution events have been identified using co-located measurements of carbon monoxide. In this study, measurements thought to be affected by pollution events have been excluded. This technique is under active refinement.

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.

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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.

7.2 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 8.3.1.

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 A.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 8
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.

8.1 Parameterization of unknowns

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

(8.1)

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.

8.1.1 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 8.1 and Figure B.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 B.

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 8.1 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.

8.1.2 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 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 only perform localization 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.

8.2 Physical parallelization

In CT2026 we break our analysis period into segments initialized every three years, and are 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 8.3). “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 year 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 12 months produces statistically consistent segment states. Thus the CT2026 results are composed of first-segment data from 2000 to 1-Jan-2004, at which point results from the second segment (initialized at 1-Jan-2003) are imposed. This process is continued to stitch together results from all nine segments.

8.3 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

(8.2)

and

(8.3)

where the prior value of the scaling factors for timestep t is λ⁻[t], the posterior at timestep t− 1 is 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:

(8.4)

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

8.3.1 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.

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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. This is made evident in the “CT2011 through CT2017” trace in the lower panel of Fig. 8.1. As it turns out, these biases were mostly due to our original short assimilation window length (Sec. 8.1.2) and the convective flux problem discussed in Sec. 6.2. 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 Fig. 8.1.

8.3.2 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 7.2). 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⁻:

(8.5)

8.3.3 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 9
Statistical performance of CT2026

9.1 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 3% (115,756 measurements out of about 4.2 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 1.4. This is quite similar to the same statistic for assimilated data, which is 1.3 (see Table ??).

These slightly inflated χ² values are actually as intended. They indicate that the model-data mismatch values used in CarbonTracker are too small. This indicates that the RMSE deflation described is Section 7.2 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 10
Resources and References

• Jim Randerson research group

• Global Fire Emissions Database (GFED) web page

• NASA GFED_CMS CASA project

• Olson ecosystem types

• Global Fire Emissions Database (GFED) web page

• 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

• NOAA Pacific Marine Environmental Laboratory

• Ocean Acidification

• GML Carbon Cycle Program

• WMO/GAW Report No. 168, 2006

Bibliography

Appendix A: Performance by dataset

Table A.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 R values assigned to dataset observations by our “adaptive” model-data mismatch scheme (Sec. 7.2). 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 B: Ecoregions in CarbonTracker

B.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 B.1, Figure B.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 B.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.

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B.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.

B.3 Ecosystems within Transcom regions

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

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