Constraining a data-driven CO<sub>2</sub> flux model by ecosystem and atmospheric observations using atmospheric transport

Upton, Samuel; Reichstein, Markus; Peters, Wouter; Botía, Santiago; Nelson, Jacob A.; Walther, Sophia; Jung, Martin; Gans, Fabian; Haszpra, László; Bastos, Ana

doi:https://doi.org/10.5194/egusphere-2025-2097

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https://doi.org/10.5194/egusphere-2025-2097

Preprints

20 May 2025

| 20 May 2025

Constraining a data-driven CO₂ flux model by ecosystem and atmospheric observations using atmospheric transport

Samuel Upton, Markus Reichstein, Wouter Peters, Santiago Botía, Jacob A. Nelson, Sophia Walther, Martin Jung, Fabian Gans, László Haszpra, and Ana Bastos

Abstract. Global estimates of the terrestrial land-atmosphere flux of CO₂ (NEE) from data-driven models differ widely depending on their underlying data and methodology. Bottom-up models trained on eddy-covariance data are most informative at the ecosystem-level. Top-down models, such as atmospheric inversions, produce regional and global results consistent with the observed atmospheric growth rate, accurately capturing the interannual variability (IAV) of NEE. Both approaches have limitations estimating NEE across scales: Bottom-up models can miss large-scale dynamics of NEE when aggregated globally. Top-down approaches have difficulty relating the large-scale atmospheric signal to biophysical processes at smaller scales. To address these limitations, we create a model that uses a hybrid combination of direct observations and atmospheric dynamics to integrate ecosystem-level eddy-covariance data and atmospheric CO₂ mole fraction data into a single coherent ecosystem-level flux model.

Aggregated globally, our new model estimates an annual sink with a low bias, and consistent IAV when compared with independent estimates. The IAV of the estimated NEE is closer in magnitude to an ensemble of atmospheric inversions, and our model produces a higher temporal coefficient of correlation with these data than state-of-the-art bottom-up data-driven models. This improvement in IAV is achieved without direct access to the observed variability of the atmosphere: the model is trained using only one year of daytime observations from 3 tall-tower observatories. No atmospheric information is available to the model during the production of global NEE estimates. This shows the efficiency of our method in synthesizing top-down information into bottom-up mapping of flux-environment relationships.

Received: 05 May 2025 – Discussion started: 20 May 2025

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Samuel Upton, Markus Reichstein, Wouter Peters, Santiago Botía, Jacob A. Nelson, Sophia Walther, Martin Jung, Fabian Gans, László Haszpra, and Ana Bastos

Status: final response (author comments only)

RC1:
'Comment on egusphere-2025-2097', Anonymous Referee #1, 12 Jun 2025
The authors present a novel approach to enhance the state-of-the-art data-driven NEE estimation system, X-BASE, by incorporating atmospheric constraints. The newly developed system, EC-STILT, addresses key limitations of X-BASE—specifically, the overestimation of the global total terrestrial sink and the underestimation of NEE interannual variability (IAV)—while retaining the valuable strength of providing fine-scale spatial distributions of terrestrial carbon fluxes, a feature often lacking in traditional inverse modeling approaches. Thus, this study is to be of broad interest to both data-driven modeling and atmospheric inversion communities. However, before publication, I encourage the authors to address several points regarding the system configuration and interpretation of the results.

Major comments
The authors should more clearly explain how EC-STILT, using only one year of data from each of the three atmospheric CO₂ observation sites, was able not only to correct biases in global NEE but also to more than double the global total NEE interannual variability (IAV) compared to X-BASE. In the annual regional NEE estimates, EC-STILT shows larger deviations from inversion estimates than X-BASE in regions with atmospheric constraints, such as the Eurasian Boreal and South American Tropical regions. Meanwhile, regions without direct atmospheric constraints—such as South American Temperate, Southern Africa, and Tropical Asia—show substantial increases in NEE IAV, contributing significantly to the increase in global IAV. Based on these results, it is difficult to understand how atmospheric constraints led to improved global NEE estimates and their IAV.

The authors state, “This is because EC-STILT learns its land-surface response in environmental space of the features instead of in geographic space like an inversion.” If this interpretation is correct, then the neural network within EC-STILT adjusts biome-specific NEE sensitivities to environmental drivers (e.g., temperature or moisture) in a way that minimizes the loss function. For example, the model may predict stronger NEE sensitivity to moisture in tropical forests, leading to increased IAV in regions with high moisture variability. But does this sensitivity enhancement improve IAV only in some regions within a biome and not others, due to spatial heterogeneity? While the neural network may function as a black box, I believe the authors could still provide further insight based on available model outputs. For example, exploring differences in learned climate/environmental sensitivities of NEE between EC_STILT and X-BASE by regions and/or biome types could help readers better understand why the model produced the observed results.

It is unclear why the authors chose to use only three tall-tower atmospheric CO₂ observations, given the availability of long-term surface, aircraft, and satellite-based datasets. Was there a decrease in model performance when more observations were included? Or was the goal to test the efficiency of the system using a minimal number of atmospheric constraints?

The current EC-STILT system shows substantial regional deviations from inversion-based estimates, with higher RMSE than X-BASE in some regions. While inversion estimates are not ground truth, this suggests that the information from just three sites may be insufficient to improve regional NEE distributions. Although the authors mention plans to address this in future work, it would strengthen the manuscript to provide at least a preliminary assessment—such as how results change when incorporating background in-situ measurements from NOAA’s ObsPack data.

Detailed comments
Line 2: The phrase "terrestrial land–atmosphere flux of CO₂" seems to refer more closely to net land flux or net biosphere exchange rather than net ecosystem exchange (NEE). I suggest using “net ecosystem exchange” to make the intended meaning clearer.

Lines 11–17: As noted earlier, while your study effectively reduces global NEE biases and improves interannual variability using a limited number of atmospheric CO₂ observations, it also leads to increased regional biases—assuming that inversion estimates are reasonably close to the truth. Since a broader set of atmospheric CO₂ data is available, including surface, aircraft, and satellite observations, it seems likely that incorporating more of them could improve both global and regional NEE estimates. Could you clarify why only a limited set of atmospheric observations was used in this study?

Lines 62–71: You mention a key limitation of the previous work by Upton et al. (2024)—that the additional atmospheric information was aggregated and provided no added value for resolving the spatial distribution of NEE. How your EC-STILT approach overcome this limitation? Could you explicitly discuss which aspects of EC-STILT (i.e., global and regional NEE estimates and their IAV) show improvement over the previous work, which do not, and what underlying factors might explain these differences.

Line 125: As you discuss later in the manuscript, inversion-based terrestrial biosphere flux estimates include not only fire emissions but also lateral fluxes. Since your study assumes that NEE corresponds to the inversion estimate with fire emissions removed, it would be helpful to state this assumption clearly at this point in the text.

Line 176: Please provide more detail on how the lateral boundary conditions for the region are derived from the 3D CO₂ fields provided by Jena CarbonScope, and how these are applied in Equation (1).

Lines 205–206: The way uncertainty is defined and prescribed seems to be a critical component of your system, but the explanation provided is not sufficiently detailed. Could you clarify how uncertainties were defined in your framework, and how the relative weighting between atmospheric constraints and eddy-covariance observation constraints was determined?

Lines 233–234: The phrase “with only local driver variables, and no atmospheric information” is somewhat unclear. It would be helpful to revise this sentence to more specifically describe what is meant by “local drivers” and “no atmospheric information”.

Figure 4: Please consider adding a panel showing the annual mean NEE from X-BASE, so that readers can directly compare it with the EC-STILT results. Additionally, for the panel showing the difference between EC-STILT and X-BASE, it would be helpful either to adjust the colorbar style or to use the same colorbar range as in Figure 4A to facilitate visual comparison.

Table 1 and Figure 5: Some values in the text, table, and Figure 5 are inconsistent. Also, bold formatting in Figure 5 seems to incorrectly indicate better performance in some cases—for example, the annual RMSE for Australia. Please review and correct these issues.

Lines 291–292: The statement “EC-STILT has modified its response by biome” should be supported by a clearer explanation in the Methods section. Does this mean that the relationship between driver variables and NEE is trained and applied in a biome-specific manner? If so, please clarify how this is implemented.

Lines 292–293: The sentence “When IAV is broken down by month (Fig. 7) across boreal and temperate regions, the increases in monthly IAV occurs during the growing season while in tropical regions show a change during the dry season” is interesting. Could you provide a potential explanation for this pattern, or at least discuss possible mechanisms that might be driving these seasonal differences across regions?

Lines 300–303: Could you clarify which figure or table supports this part of the text?

Figure 8: Some of the values shown in the figure do not match those reported in the main text. Please review and correct these inconsistencies.

Line 330: Since the concept of “environmental response” is a central and novel aspect of your system, it would be helpful to provide a more detailed explanation of how this is defined and implemented in the Methods section. This would help readers better interpret your results.

Lines 345–347: Table 1 suggests that the limited atmospheric observations used in your study are not sufficient to effectively embed the atmospheric signal into the EC-STILT ecosystem response or to guide the spatial and temporal distributions of the estimated NEE.

Lines 379–381: It would be helpful to include supporting results for this statement maybe in the supplementary material.
Citation: https://doi.org/10.5194/egusphere-2025-2097-RC1
RC2:
'Comment on egusphere-2025-2097', Anonymous Referee #2, 24 Jun 2025
Referee report:
Title: “Constraining a data-driven CO₂ flux model by ecosystem and atmospheric observations using atmospheric transport”
Author(s): Samuel Upton et al.
MS No.: egusphere-2025-2097
MS type: Research article
The manuscript presents a novel approach for estimating CO₂ fluxes by designing a data-driven model which utilises constraints from both eddy-covariance measurements and atmospheric CO₂ observations. The study attempts to overcome the drawbacks of current flux estimates by improving the inter-annual variability estimations of bottom-up models (e.g., FLUXCOM X-BASE) with the help of atmospheric CO₂ observations. Even though the approach has significant potential for future CO₂ flux estimations, I have a few concerns which need to be addressed before publication of this manuscript.
Major comments:
The authors claim that the inclusion of atmospheric CO₂ observations from three sites in their model design improved CO₂ flux estimates in terms of capturing inter-annual variability (IAV). Due to the unavailability of observational estimates, they compared their outputs with an ensemble of inversion results and reported that the IAV values for those two are closer compared to X-BASE simulated values.
But the authors did not explain how atmospheric CO₂ observations covering only one year from these three sites add IAV to the model outputs? Further, it is not clear why they did not use other atmospheric CO₂ observations (from additional sites) and/or observations covering a longer period than just one year. It is not clear what are the limiting factors for using more atmospheric observations. At this stage, it is not convincing that these limited data can provide inter-annual constraints for simulated outputs.

It should be noted that the reported correlation values are significant (R² = ~0.4) but rather weak. This needs to be discussed and put into context. Further, the regional comparison shows that regions without atmospheric constraint (e.g., Southern Africa) show higher correlation values than regions with atmospheric constraint ( e.g., Europe - HUN). How can this be explained?

I am also curious about why the performance of EC-STILT with regard to IAV is not improved much in the European region, even if the atmospheric constraint is available. Again, this needs to be explained and discussed in the manuscript.

Furthermore, the relative weights (𝝎_EC and 𝝎_ATM) in the objective function play an important role in constraining the model. For a reader to better understand the constraints, these weights should be provided and explained for each region.

Detailed comments:
L89: A map of the locations of eddy-covariance towers used for the study may be included, which will provide an understanding of the data availability around the globe.

L143: Authors did not properly explain what are the driver variables used in their model to estimate CO₂ fluxes (NEE). A table of driver variables used in the EC-STILT model and their sources should be included.

L192: It is not clear how the authors calculate the LBC and ocean components for each CO₂ observation. Is it with the help of STILT footprints?

L193: How is NEE_Land estimated? Here, it is not clear how the ecosystem-model is designed for points where there are no eddy-covariance observations.

L208: The authors should explain the back-propagation process with more clarity. It is not clear from the description which and how parameters are getting updated. Also, I think Figure 1 can be improved further to incorporate back-propagation in the final stage.

L235: How is IAV calculated?

L442: What are examples of the ‘meaningful non-biogenic flux’ terms that are not included? And how would these bias the results?

Minor comments:
L26 and further occurences: Nelson* and Walther* et al., 2024 -> Nelson et al., 2024

L40 and further occurences: Walther* and Besnard* et al., 2022 -> Walther et al., 2022

L75: Time-inverse -> Time-Inverted

L114: Integrated Carbon Observatory System -> Integrated Carbon Observation System

L126: RANDERSON et al., 2017 -> Randerson et al., 2017

L193: ΔPPMfoot need to be properly defined (preferably using an equation).

L199: SL (Eq. 6) -> (Eq. 7)

L245: Fig. 3 C -> Fig. 4 C

Table 1, Figures: Please use the same precision as in the description.

L333-335: I suggest splitting this sentence into two for better readability.
Citation: https://doi.org/10.5194/egusphere-2025-2097-RC2

Samuel Upton, Markus Reichstein, Wouter Peters, Santiago Botía, Jacob A. Nelson, Sophia Walther, Martin Jung, Fabian Gans, László Haszpra, and Ana Bastos

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Short summary

We create a hybrid ecosystem-level carbon flux model using both eddy-covariance observations and observations of the atmospheric mole fraction of CO₂ at three tall-tower observatories. Our study uses an atmospheric transport model (STILT) to connect the atmospheric signal to the ecosystem-level model. We show that this inclusion of atmospheric information meaningfully improves the model's representation of the interannual variability of the global net flux of CO₂.


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Constraining a data-driven CO2 flux model by ecosystem and atmospheric observations using atmospheric transport

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Constraining a data-driven CO₂ flux model by ecosystem and atmospheric observations using atmospheric transport