the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 11 Sep 2026
Tidal forcing causes bi-decadal variability in dissolved oxygen: clarification with a causal discovery method
Abstract. Identifying the mechanisms behind the trends and variability in observations of ocean oxygen concentration (O2) is key to understanding long-term ocean deoxygenation. But this task remains challenging, as observations contain persistent signals from interacting physical and biogeochemical processes. Here we apply the time series causal discovery method, PCMCI, to a dataset of O2 from the Oyashio region in the North West Pacific to test whether a causal relationship from the nodal cycle in the tidal forcing on to the O2 exists. We identify causal links from the tidal index to O2 and apparent oxygen utilisation (AOU), concentrated between approximately 27.35σθ and 26.75σθ, with a characteristic lag of approximately two years. The tidal effect on O2 is only present at densities greater than the density of the late-winter mixed layer (the base of the mixed layer), with a maximum causal link at around 27.1σθ. Little evidence is found for a causal relationship with the O2 solubility. Compared to lagged correlation, PCMCI detects a reduced strength and density distribution of the tidal effect and removes much of the lag structure while retaining the characteristic 2 year lag. The density and lag structure are consistent with transport and enhanced tidal mixing from within the Sea of Okhotsk system and the Kurils, but we cannot identify a geographical location or the complete physical pathway of the causal effect with the existing observations. It may be the case that several causal models are compatible with the existing data. These results show the promise of causal inference and discovery methods within oceanographic problems.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-5168', Anonymous Referee #1, 12 Oct 2026
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RC2: 'Comment on egusphere-2026-5168', Anonymous Referee #2, 23 Oct 2026
Blackledge et al. apply the causal discovery method PCMCI to the Oyashio O2 record (1954-2018) to test whether the 18.6-year nodal tidal cycle drives the observed bidecadal O2 oscillations. They find links from a tidal index to O2 and AOU at 26.75-27.35 σθ with a 2-year lag, confined below the late-winter mixed layer and with little evidence of a solubility effect. They interpret this as consistent with tidal mixing in the Sea of Okhotsk and the Kuril Straits. Exploring how the nodal cycle interacts with ocean O2 below the mixed layer is an interesting scientific topic and would be of interest to the audience of Biogeosciences. However, I do not think this manuscript provides convincing evidence for the causal relationship claimed in its title. The analysis identifies a lagged statistical association, while the physical mechanism remains unresolved. I also think the presentation in this manuscript is quite difficult to follow, particularly in the Methods and in how the physical results and mechanism are discussed. Therefore, I do not recommend publication in its current form.
Major comments:
- The main message is not delivered clearly. The Results and Discussion focus on the properties of the PCMCI output (link strengths, lags and comparison with lagged correlation), while the physical signal itself is shown only briefly, and the mechanism is discussed mainly by listing possible pathways (Fig. 12) without linking them to the specific findings. The tone is also more confident about causality than the analysis supports. PCMCI identifies a lagged statistical dependence on an exogenous index, and the authors acknowledge that the physical pathway cannot be identified from these data. A mechanistic approach is needed to connect the statistical result to a cause, for example a regional model with explicit tides run with and without nodal modulation under repeat-year forcing, testing whether it reproduces the observed density range, ~2-year lag and AOU response. At a minimum, the results should be compared with existing simulations of nodal tidal mixing in this region (Osafune and Yasuda, 2006, 2013). I recommend restructuring the Results and Discussion around the physical result, and revising the title, abstract and conclusions to describe a statistical association consistent with tidal forcing rather than a demonstrated cause.
- The Methods section is hard to follow. Several points are repeated across sections, and the wording is unclear. Section 2.2 reads as a general introduction to causal discovery, and the workflow is spread across Sections 2.1, 2.3 and 3.4-3.5, with PCMCI and the bootstrap first appearing in the Results. I suggest opening the Methods with a short step-by-step description or schematic of the analysis. Key choices are also not described clearly enough to reproduce. Most importantly, the tidal index includes a noise term from tide-gauge residuals, which contain weather and circulation signals. The preprocessing, the handling of missing data, and data issues should also be specified and discussed.
Minor comments:
Title and L6–7: "Causes" overstates what a statistical association can show (Major Comment 1).
L83 and P23, L405: Figure 1c is cited, but Figure 1 has only panels (a) and (b).
L89–91: "A large and direct role" seems too strong given the modest explained variance and the mediated pathways proposed in Fig. 12. Consider "a measurable role".
L112–114: "18.6 frequency" should be "18.6-year period".
L133–134: "over time scales over time scales" is duplicated.
L155–159: The instrument changes (thermometers to CTD in 1989-1990; modified Winkler titration from 1994) could introduce step changes that alias into low-frequency variability. Also, thermometers were used "until January 1989" but CTDs were "not employed until after 1990"; what was used in between?
L166–167: Spatial offsets between cruises of ~3 µmol kg-1 are similar to the amplitude of the oscillation at 27.00σθ (Fig. 4d). Could you discuss how this affects the result?
L168–174 and Figure 4: Seasonal coverage changes over time, with sparse winter sampling and very sparse data after about 2010. Could you describe how missing seasons were handled in PCMCI and report the effective sample size at each level.
L177–178: Could you clarify "a polynomial fit to all levels above 26.8σθ" (above in density or in depth?), how the trend was removed, and how this combines with standardization "by month" (L265) for seasonal data.
L185–193 and P11, L194–196: Could you specify which tidal constituents the index represents and with what sign (the nodal modulations of K1/O1 and M2 have opposite phase), and how an 18.61-year cosine is obtained from gauges with records as short as 9 years. The added noise term comes from sea-level residuals, which contain weather and circulation signals rather than tides. Could you clarify whether the index allowed autodependencies in PCMCI, and repeat the O2 analysis with a purely astronomical index and with the noise component alone, as in Fig. 11b.
L192–193: The tide gauges are shown in Figure 1a, not Figure 1b.
Figure 2 caption: The temperature curve is in panel (a), not (c).
L283: "Figure 5a, c and d" should be "Figure 5a, c and e".
Table 1: MCI is a partial correlation and ranges from -1 to 1 (the AOU values are negative), not from 0 to 1.
Figure 5e: PCMCI finds NPGO -> PDO at lag 1 in the O2sat graph but not in the O2 or AOU graphs, although the climate indices are identical in all three. This contradicts L359 ("no causal links between these indices").
Table 2: I think several entries do not match the figures. For example, the O2 PCMCI range starts at 26.85 σθ in Fig. 6a, not 26.75.
L302–304: "MCI ≈0.4 versus ≈0.3" does not match Table 2 (0.46 and −0.43) or Fig. 7a (-0.30 to -0.43). Could you also clarify what "clear asymmetry" refers to at α = 0.05.
L306: "Figure 7b" should be "Figure 7a".
L324–325: "Almost entirely explains" contradicts the ~21% of variance stated at L434.
L341 and L348–349: Eq. (4) has only the tidal index as a parent, and Fig. 5a shows no O2 autodependency, yet L348-349 refers to "the tidal link and an auto-dependency". I am a bit confused here.
L405; P25, L411; P28, L484: "Robust causal effect", "well explained" and "robust causal links" are not supported by a robustness test.
L439–444: You might want to compare the results with existing model studies of nodal tidal mixing in this region (Osafune and Yasuda, 2006, 2013), in terms of amplitude, lag and density range.
L471: "the the" is duplicated.
Figure 12 caption: "more than on" should be "more than one".
L507: The Zenodo DOI is still a placeholder ("[zenodo archive]").
Figure A1 caption: The panel labels are inconsistent ("Causal (a, b, c)" but "O2 (a, b)"). How does this figure differ from Figure 5?
Citation: https://doi.org/10.5194/egusphere-2026-5168-RC2
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- 1
Review for “Tidal forcing causes bi-decadal variability in dissolved oxygen: clarification with a causal discovery method”
Blackledge et al.
Major Comment: Reliability and validation of the PCMCI-based causal inference
The application of PCMCI to historical O₂ observations is potentially interesting. However, I have fundamental concerns about the reliability of the inferred causal relationships and whether the main objective of this study has been achieved.
The central issue is that the authors have not independently demonstrated that PCMCI can reliably identify the physical causal relationships underlying O₂ variability in the Oyashio region. The causal network includes tidal forcing and climate indices such as PDO, NPGO, and NPI, but excludes important biogeochemical processes, including biological production, organic matter remineralization, and respiratory O₂ consumption. Consequently, the detected Tide → O₂ relationship may reflect either direct physical processes or indirect effects mediated by biological and biogeochemical processes. The present analysis cannot distinguish between these possibilities.
Furthermore, the simplified structural causal model (SCM) constructed from the PCMCI results reproduces the observed lagged correlations, but this does not constitute an independent validation of the inferred causal structure. Different causal mechanisms can produce similar statistical relationships. Therefore, the physical interpretation of the detected causal links remains uncertain.
In my view, the reliability of the PCMCI-based causal inference should be established before applying the method to historical observations and interpreting the results as evidence of physical causality. For example, the authors could first apply PCMCI to numerical ocean model output including the Oyashio region, where causal pathways can be independently evaluated through controlled experiments, and examine whether the method correctly recovers the relevant relationships. The analysis could then be repeated using subsampled model output that mimics the limited variables and sparse temporal coverage of the observations. Such experiments would provide a more convincing assessment of the reliability of the proposed methodology.
I am also concerned about the overall structure of the manuscript. Considerable space is devoted to explaining and justifying the PCMCI methodology, whereas the physical interpretation and independent validation of the main findings remain insufficient. As a result, the manuscript lacks a clear and convincing progression from the research objectives to the results and conclusions. If the reliability of the inferred causal relationships were established, much of the technical description of PCMCI could be moved to an Appendix, allowing the main text to focus more clearly on the scientific findings.
Overall, I do not consider that the manuscript has yet achieved its primary research objective, because the reliability and physical significance of its central causal inference have not been adequately demonstrated. I therefore recommend that the authors first establish the validity of their causal-discovery approach through independent testing before drawing conclusions about the physical mechanisms controlling O₂ variability in the Oyashio region.
I’m not sure if this will be of any use at the moment, but I’ll note down the points I’ve noticed as minor comments.
Minor Comments
I also suggest considering a simpler presentation using time-series plots. For example, Navarra et al. (2026), who also applied PCMCI, presented their results using time-series plots in Figure 4. A seasonally separated time-series presentation might make the results easier to understand and interpret.