| 08 Aug 2025
Improving coastal ocean pH estimates through assimilation of glider observations and hybrid statistical methods
Abstract. Ocean acidification monitoring and carbon accounting require accurate estimates of marine carbonate system variables, particularly in dynamic coastal regions where observations remain sparse. This study presents an approach to improving carbonate system state estimates in the California Current System through the assimilation of underwater glider observations with both dynamical and statistical models. We implement a 4D-Var data assimilation system that jointly assimilates physical variables, chlorophyll, and glider-based pH and alkalinity data into a regional coupled physical-biogeochemical model. Our results demonstrate that joint assimilation of carbonate system variables successfully improves pH and alkalinity estimates while maintaining the quality of physical and chlorophyll estimates. Cross-validation experiments reveal that pH data assimilation typically improves estimates near the observation network, although downstream advection of increments can occasionally degrade results. We also show that hybrid estimates that combine the output of the dynamical, physical ocean model with a statistical model produce accurate carbonate system estimates without requiring a biogeochemical model. This finding suggests that physical ocean models and data assimilation systems can obtain reasonable carbonate system estimates by combining statistical methods with model estimates of temperature and salinity.
This manuscript presents a rigorous and timely assessment of how glider-based carbonate-system observations can improve coastal pH estimates through 4D-Var assimilation in ROMS–NEMUCSC. The integration of pH and alkalinity with physical and chlorophyll data, combined with a thorough evaluation of ESPER-based hybrid estimates, makes this contribution relevant for coastal carbon monitoring and DA system design.
Overall, the study is technically strong, clearly motivated, and generally well executed. The comparison between full biogeochemical DA and hybrid statistical–dynamical methods is valuable and will interest both modeling and observational communities. The manuscript is publishable after major revisions aimed at sharpening key messages and clarifying methodological choices.
Major comments
1. The manuscript is rich in experiments, but the core scientific conclusions could be distilled more explicitly. The three main findings (limited impact of physical DA on pH, strong improvement from pH+alkalinity DA, and competitive performance of hybrid ESPER approaches) should be highlighted earlier and revisited more succinctly in the Discussion.
2. The necessity to assimilate estimated, not measured, alkalinity (Section 2.6) is a central limitation. The discussion acknowledges this but remains somewhat cautious. The authors should explicitly quantify the sensitivity of the pH increments to TA uncertainty and clarify in which coastal regimes the ESPER TA is reliable, and where it may fail (river plumes, OM-rich waters, denitrification).
3. Some cross-validation experiments show deterioration of pH downstream of the lines, attributed to advection of increments. This is important for future glider network design. A brief dynamical explanation (e.g., density structure, mesoscale features along Line 67) would strengthen the argument.
4. The result that hybrid ESPER estimates outperform the full BGC model (when carbonate variables are not assimilated) is striking. The implications deserve more emphasis: under which conditions does a hybrid approach suffice operationally? Is the benefit solely from improved T–S via physical DA, or also from limitations in the NEMUCSC carbon module?
5. The study shows an expected improvement when O2 is assimilated, but the weak coupling between pH and O2 increments reflects structural constraints of the DA system. It would be beneficial to comment on whether variable-covariance specification (currently set to zero) is a limiting assumption for future biogeochemical DA.
6. The manuscript relies exclusively on ESPER for alkalinity and DIC estimation, but does not justify this choice. This is important because CANYON-B/CONTENT is widely used in the community, specifically trained for glider-type variables, and often performs better in coastal and upwelling systems due to its inclusion of oxygen and sometimes nitrate as predictors. The authors should briefly explain why ESPER was selected, and whether alternative empirical regressions (e.g., CANYON-B, LIAR, multi-sensor neural networks) were evaluated. A short comparison or rationale would strengthen confidence in the robustness of the hybrid approach. At minimum, please clarify: what variables ESPER requires in this implementation, whether CANYON-B was unsuitable due to predictor availability or training domain, whether differences between algorithms could alter the conclusions on hybrid performance.
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Minor comments
-Figures 4 and 5 are informative but visually dense; consider simplifying color scales or moving supplementary diagnostics to the Appendix.
-State the glider pH sensor accuracy explicitly when first introduced (currently only in Table 3).
-Clarify whether ESPER was re-trained or used as published.
-The manuscript is long; some methodological descriptions (e.g., NEMUCSC structure) could be tightened.
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