the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 04 Jun 2026
Furthest-first inversion for internal consistency adjustments in the biogeochemical data product GLODAPv3
Abstract. The global ocean absorbs a significant portion of anthropogenic carbon dioxide (CO2) emissions. Tracking the fate of absorbed CO2 and its impacts requires an internally consistent global observational dataset spanning decades. In the Global Ocean Data Analysis Project (GLODAP), data from disparate research cruises are compared in a secondary quality-control process, adjusted for consistency where necessary and compiled into a data product. Differences between cruises are quantified with a crossover analysis, comparing data at depth (where natural variability is minimal) from nearby sampling stations, and an inversion algorithm calculates a set of adjustments that would minimise these differences globally. The adjustments are reviewed by an expert committee and a subset applied to produce the final data product. The previous major version (GLODAPv2) used a weighted least squares (WLSQ) approach for the inversion. However, several issues became apparent when applied to the GLODAPv3 dataset, primarily significant regional biases in calculated adjustments. To address these issues, a new inversion algorithm called furthest-first (FF) has been developed for use in GLODAPv3, which has been implemented in a freely available, open-source Python package (xover). Here, we describe the FF approach and test it on simulated datasets and by comparing it to WLSQ, finding that it produces accurate adjustments. We also show how the FF approach can be adapted (i) to avoid the regional biases that appear in WLSQ, (ii) to find an optimal set of adjustments accounting for the fact that some cruises will ultimately not be adjusted, and (iii) to approximately preserve selected trends in the cruise-by-cruise differences. Points (i) and (ii) above are addressed by a two-step variant of the approach denoted FF2, which was applied in GLODAPv3. While FF represents a marked improvement on WLSQ for the GLODAP application, no algorithm can completely replace the role of expert judgement in the inversion process, for example when selecting convergence criteria, which cruises are permitted to be adjusted, and which trends should be preserved.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Ocean Science.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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Status: open (until 30 Jul 2026)
- RC1: 'Comment on egusphere-2026-3063', Denis Pierrot, 09 Jul 2026 reply
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Recommendation: Accept as is. However, I hope the authors will consider the specific and technical comments.
General Comments:
The article describes in detail a new mathematical method called “Furthest First” to calculate the optimal adjustments to apply to measured parameters on individual cruise and produce an internally consistent data product, the Global Ocean Data Analysis Project version 3 (GLODAPv3) which spans decades of surface and interior biogeochemical observations around the globe.
GLODAP is fundamental to tracking how the ocean functions as the planet's primary climate buffer. By providing a standardized, three-dimensional view of the ocean interior, it allows scientists to measure how much human-induced stress the marine environment is absorbing and how those changes alter global climate feedback loops. It helps quantifying the ocean carbon sink, assess ocean acidification and ground-truth climate projections. Improving the quality of the product is crucial for science and it validates the purpose of this article . It correctly mentions that it does not pretend to improve the accuracy of the product but simply the internal consistency, which is all this exercise can hope for, while reducing the possibility of regional or other biases and preserving as much as possible the potential trends present in the data.
The reviewed article is very well-structured, providing a clear and logical progression that enhances its overall readability. It effectively begins by identifying the critical limitations and unresolved issues of the previous methodology, establishing a strong justification for the study. Building on this foundation, the authors clearly explain how their newly proposed method directly addresses and resolves these historical shortcomings, specifying that a major advantage is its iterative approach to determining adjustments, which optimizes data refinement. The methodology itself is described with excellent detail, ensuring the approach is transparent and reproducible. Furthermore, the authors effectively demonstrate that the new method is particularly well-adapted to the flexibility required for such an exercise. They clearly explain how it leaves essential room for field oceanographers to weigh in, and limit adjustments made to specific cruises based on scientific criteria.
The clear description of the methodology effectively demonstrates why this approach is perfectly tailored to the problem at hand. Importantly, the authors provide a clear rationale for why the mathematical results are entirely sound from a biogeochemical perspective.
The proposed methodology is sound, and its validation via simulated data clearly demonstrates its superiority over the previous approach. This work holds notable scientific significance because it improves a data product of wide importance to the community. Structurally, the manuscript is excellent, featuring concise language that demonstrates the authors' expertise. The availability of the open-source code ensures robust reproducibility and allows the method to be seamlessly applied to future datasets, maximizing its scientific utility.
Specific comments:
I only have a couple comments about sections I found were not very clear to me.
If that’s the case, I am not clear why this would mean the “…differences between basins probably reflect random uncertainties in cruise pair offsets in the connecting cruises, which do not average out to zero because of the scarcity of connections, rather than true regional biases that should be removed with adjustments.”
Technical corrections: