the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 02 Sep 2026
Identifying Drivers of Sea Surface pCO2 via the Lag-Convergent Cross Mapping Model
Abstract. In the context of global climate change, analyzing the driving factors of key ocean carbon cycle parameters is crucial for accurately quantifying ocean carbon sink capacity. The Convergent Cross-Mapping (CCM) method provides an effective approach for causal inference in nonlinear systems, yet it cannot characterize the ubiquitous time-lag effects within ocean carbon cycle systems, which readily results in underestimated causal strength and misidentified causal relationships. To address this limitation, this study incorporates the causal time-lag parameter (Lc) into the CCM framework as an optimized variable, and proposes a Lag-Convergent Cross Mapping (L-CCM) approach that accounts for optimal causal time lags, thereby constructing a time-lag embedded causal inference model. Taking the subtropical Northwest Pacific as the study domain, this study combines monthly causal screening and daily quantitative time-lag analysis to identify 18 potential drivers of sea surface pCO₂. Results show that L-CCM detects optimal causal time lags, under which the average causal strength of all drivers increased by 10.32 %. Strong causal drivers of sea surface pCO₂ include sea surface temperature (SST), sea surface salinity (SSS), chlorophyll a concentration (Chl), pH, etc., whereas weak causal factors cover surface zonal and meridional currents (Uo, Vo), zonal and meridional geostrophic currents (Ugos, Vgos). This method effectively reduces underestimation and misidentification of causal links, offers a reliable framework for ocean carbon cycle causal analysis, and holds promise for wider applications.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2026-3875', Anonymous Referee #1, 07 Sep 2026
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AC1: 'Reply on RC1', Min Liu, 11 Oct 2026
;;;;;;;;;; General comment
In this manuscript authors present methods (CMM and L-CMM) to investigate the drivers of the oceanic surface pCO2. This is applied in the North-West Pacific subtropical region using SOCAT and CMES data-sets for the period 2000 to 2020. Authors conclude that “SST, Si, PO43-, O2, TCO2 and TALK serve as core dominant drivers of pCO2 variation”. I guess such result is known since decades (e.g. Takahashi et al 1993, 2002). What is new here and how this helps interpreting the processes that drive the ocean CO2 cycle (and air-sea CO2 fluxes) ? As the results confirm many previous studies and because authors have in hand the global SOCAT data-set, I suggest the authors extend their analysis to the global ocean, e.g. applying the methods to all biomes (Fay and McKinley, 2014)
In its present form the paper is not suitable for publication and need major revision. Figures need to be revised and I think some figures are missing. A list of the data-sets used should be presented in a table with associated references. I’ve listed below specific comments and questions.Response: We sincerely thank the reviewer for this important and constructive overall assessment of our manuscript. We agree that the roles of temperature, carbonate-system properties, nutrient-related processes, and biological activity in regulating surface-ocean pCO2 have been well established through decades of observational, mechanistic, and process-based studies. Therefore, we do not regard the identification of these variables as important controls on surface-ocean pCO2 as a new oceanographic finding in itself. We recognize that this distinction was not sufficiently clear in the original manuscript, which may have placed too much emphasis on the “identification and ranking” of the driving factors. We will clarify this point in the revised manuscript.
The contribution of this study lies in both the methodological and diagnostic aspects. Building on CCM, we developed and implemented an L-CCM framework in which the variable-specific causal time lag, Lc, is explicitly treated as an optimization parameter. This framework characterizes the dynamical coupling between pCO2 and each candidate variable, allowing not only the strength of the inferred causal relationship to be quantified through cross-mapping skill, but also the corresponding optimal time lag to be determined. The primary objective of this study is therefore to characterize the nonlinear dynamical relationships between surface-ocean pCO2 and multiple physical and biogeochemical variables, with particular emphasis on differences in their time-lag characteristics. In a coupled ocean system, different processes do not necessarily influence surface-ocean pCO2 synchronously. Some relationships may exhibit short or nearly synchronous coupling, whereas others may become more apparent only after an appropriate temporal offset is considered. In this sense, the recovery of several well-established controls on pCO2 mainly provides an oceanographically meaningful consistency check for the inferred dynamical relationships, whereas the additional information provided by this study lies primarily in the distinctly different lag-dependent coupling characteristics between individual variables and pCO2.
Our results show substantial differences in the optimal lag structures among variables, ranging from near-synchronous coupling to delays of several days or even several weeks. For some relationships, the cross-mapping skill increased markedly relative to the synchronous case when variable-specific temporal offsets were incorporated. We therefore consider the principal contribution of this study not to be the rediscovery of variables already known to influence surface-ocean pCO2, but rather the characterization of the lag structures of these relationships from the perspective of nonlinear dynamical systems, and the demonstration that some delayed dynamical relationships may be underestimated when only synchronous relationships are considered. We will make this distinction explicit in the revised Abstract, Introduction, Discussion, and Conclusions.
From an ocean-process perspective, the different lag structures add a temporal dimension to our understanding of the coupling between pCO2 and physical, biological, and biogeochemical processes. Shorter lags may reflect more rapidly expressed dynamical coupling, whereas longer optimal lags may integrate slower processes associated with mixing, transport, biological uptake and remineralization, and carbonate-system adjustment. Importantly, we interpret these optimal lags as effective dynamical timescales rather than as precise response times of any single physical or biogeochemical mechanism. Because surface-ocean pCO2 is an important oceanic state variable controlling the air–sea CO₂ partial-pressure difference, understanding the temporal structure of its variability can also help elucidate ocean-side processes relevant to air–sea CO₂ exchange. However, this study does not attempt a complete attribution of air–sea CO₂ fluxes, because the actual flux also depends on atmospheric pCO2, gas-transfer velocity, solubility, wind conditions, and other factors.
We also greatly appreciate the reviewer’s suggestion to extend the analytical framework to different ocean biogeographical regions at the global scale. We agree that such an extension would be valuable for testing the spatial generality of the inferred causal relationships and lag structures, and for examining how they differ among oceanic dynamical and biogeochemical regimes. In the present study, however, we first establish and apply a two-stage framework—long-term screening at the monthly scale followed by lag characterization at the daily scale—in a region where both long-term regional datasets and continuous high-temporal-resolution observations are available. A systematic extension of this framework to different ocean biomes globally would require further consideration of differences in observational density, temporal continuity, the degree of colocation among variables, and the underlying dynamical regimes across ocean regions. We therefore consider a global analysis based on ocean biogeographical classifications such as Fay and McKinley (2014) to be an important next step for testing the spatial transferability and regional dependence of the framework, rather than a straightforward extension of the present regional study.
In addition, we will systematically revise the figures and, where appropriate, add further information on the study region and its relevant oceanographic context. We will also add a new table summarizing the datasets and variables used in this study, together with the corresponding references.;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; Specific comments
C-01, Line 24: Authors write: ”Against the backdrop of global climate change, the ocean, as one of the largest active carbon sinks, plays a critical buffering role in the climate system by regulating atmospheric CO₂ concentrations (Tjiputra et al., 2025)”. Is Tjiputra et al., (2025) who used models relevant reference for this note. I think Friedlingstein et al, (2025) should also be refer.
Response: We thank the reviewer for this suggestion. We have revised this sentence and now cite both Friedlingstein et al. (2025), which reports the ocean carbon sink in the 2024 Global Carbon Budget, and Tjiputra et al. (2025). The revised sentence reads:“In the context of global climate change, the ocean, as one of the largest active carbon sinks, absorbs approximately one-quarter of anthropogenic CO₂ emissions (Friedlingstein et al., 2025) and plays a critical buffering role in the climate system by regulating atmospheric CO₂ concentrations (Tjiputra et al., 2025).”
C-02: Section “2.1.1 Overview of the Study Area”. A map of the region with a scheme of circulation would be useful for readers not familiar with this region. Such map could include the mean air-sea CO2 fluxes as color code.
Response: Thank you for the suggestion. We have revised the manuscript accordingly.
C-03, Line 73: Authors write: ”We focused on the subtropical waters of the northwestern Pacific (28° N–40° N, 140° E–180° E). As one of the world’s major ocean carbon sinks(Chen et al., 2025), this region exhibits substantial air-sea CO₂ exchange fluxes and is shaped by complex ocean dynamic processes, making it an ideal study area for identifying causal relationships among key components and driving factors of the ocean carbon sink.” Why focusing in the NW SBT Pacific ? In this region, it is well known that pCO2 is mainly driven by SST (e.g. Inoue et al, 1999; Takahashi et al, 2002). I think authors should list previous studies and processes identified and quantified) as main drivers of pCO2 at seasonal to multi-decadal scales.
Response: We selected this region because it is characterized by active air–sea carbon exchange and represents an important ocean carbon sink, while also being influenced by multiple physical and biogeochemical processes operating over different characteristic timescales. These features make the region well suited for examining multivariate causal relationships and their associated lag structures.
We do not regard the re-identification of well-established controls such as SST as a new oceanographic finding. Rather, these established relationships provide a physically meaningful reference for evaluating the causal structures inferred in this study. The recovery of these major known controls indicates that the inferred causal relationships are broadly consistent with existing oceanographic understanding. Building on this consistency, we further focus on the causal strength and lag characteristics of other physical, biological, and biogeochemical variables in relation to surface-ocean pCO2. Following the reviewer’s suggestion, we will add relevant previous studies of pCO2 in this region to the revised manuscript.C-04, Line 77: Authors write: ”We selected sea surface partial pressure of carbon dioxide (pCO₂) as the core parameter characterizing the ocean carbon sink, and identified its potential driving factors”. Please, explain why you prefer to select pCO2 rather than DIC that is a core parameter of the CO2 cycle (recall that pCO2 is the result of DIC, ALK and SST).
Response: We thank the reviewer for this important comment. The choice of pCO2 as the target variable does not imply that we regard it as an external response variable independent of DIC, alkalinity, or SST. Rather, our focus is on the state of surface-ocean CO₂ and its connection to air–sea CO₂ exchange. Surface-ocean pCO2 is a key ocean-side variable determining the CO₂ partial-pressure gradient between the ocean and atmosphere and enters directly into the calculation of air–sea CO₂ fluxes (Wanninkhof, 2014). Changes in pCO2 are therefore directly related to variations in air–sea CO₂ exchange and the ocean carbon sink. By contrast, DIC is an important state variable of the marine inorganic carbon reservoir, and its variations affect pCO2 through carbonate-system equilibria, thereby influencing air–sea CO₂ exchange.
The purpose of our analysis is to identify the causal coupling and associated lag characteristics between these physical and biogeochemical variables and pCO2, rather than to treat them as mutually independent controls. Our aim is not to compare whether pCO2 or DIC is more important, but to use pCO2 as the primary target variable in accordance with the specific research question addressed in this study.C-05, Line 79: Why pH is listed in the driven variables ?
Response: Both pH and pCO2 are state variables of the marine carbonate system and are jointly constrained by DIC, total alkalinity, temperature, and salinity. We included pH in the analysis not because it was assumed a priori to act as an independent physical forcing, but because it serves as a candidate variable representing the state of the carbonate system and its internal coupling.
CCM/L-CCM does not require the analyzed variables to be statistically independent. Rather, it identifies information shared among dynamically coupled variables through state-space reconstruction. Retaining pH therefore provides a useful test of whether the method can recover the strong coupling expected within the carbonate system. Following the reviewer’s suggestion, we have further clarified the role of pH in the revised manuscript and have avoided interpreting its high cross-mapping skill as evidence of an independent external causal effect of pH on pCO2. The source and independence of the pH data are further discussed in our response to C-10.C-06, Line 91: Authors write: ”The sea surface pCO₂ observations were retrieved from the Surface Ocean CO₂ Atlas (SOCAT) (Bakker et al., 2016). ” Please specify the SOCAT version and present a map of the SOCAT data you used. Specify the SOCAT data selected (both Cruises and fCO2 flags). As SOCAT data are for fCO2, did you convert the data to pCO2 ?
Response: We converted the SOCAT pCO2 data to pCO2 using a commonly applied temperature-dependent approximation. In the revised manuscript, we have explicitly added the pCO2-to-pCO2 conversion equation together with the corresponding reference, and have also provided detailed information on the SOCAT dataset used in this study.
C-07, Line 98: Authors write: ”The data spanned from 2000 to 2020 at a monthly resolution”. Why this period is selected ? Because of available data ? Other reasons (e.g. Post 1998 ENSO ?).
Response: The period 2000–2020 was selected primarily based on the common temporal coverage and data completeness across the multiple datasets, as well as the requirement of CCM analysis for a sufficiently long time series, rather than using the 1998 ENSO event as a temporal boundary. The monthly-scale analysis requires spatiotemporal matching of the pCO2 data with multiple physical and biogeochemical variables. We therefore selected 2000–2020 as the study period because the different data sources provide relatively stable overlapping coverage during this interval. After data matching and preprocessing, a total of 248 valid monthly samples were obtained, providing a sufficiently long time series for the subsequent CCM analysis.
C-08, Line 100: (b) Daily-scale Data. Original SOCAT data are also at local/daily scales. Why not using the original SOCAT data to get high frequency scale.
Response: We did not directly use the original SOCAT records for the daily-scale lag analysis because these high-frequency observations do not provide sufficiently continuous, temporally synchronized, and complete records of all variables required for the lag analysis. In particular, SOCAT does not continuously provide the full set of candidate drivers considered in this study over the same period, including variables such as pH, O₂, TCO₂, TALK, and Chl.
C-09: Figure 1 Caption: Sentences repeated.
Response: Revised accordingly.
C-10, Line 214: Authors write: ”Among these, pH and SST exhibited the highest cross-mapping skill with pCO₂, with ρ values reaching 0.9467 (pCO₂ xmap pH) and 0.8064 (pCO₂ xmap SST), respectively, indicating a tight coupling relationship between these factors and pCO₂”. I probably understand the high skill for SST in the SBT region but I don’t understand the link with pH. By the way, what are the pH data used ? I guess this is not clearly listed in the manuscript. Are the pH data independent from pCO2 ? Is it measured or calculated pH ?
Response: CCM/L-CCM does not require the analyzed variables to be statistically independent. Its underlying principle is to identify information shared among variables within a coupled dynamical system through state-space reconstruction. Therefore, the high cross-mapping skill between pH and pCO2 still indicates a strong dynamical coupling between the two variables.
We have also added information on the source of the pH data. The monthly pH data were obtained from the pH field (total scale) of the CMEMS global biogeochemical reanalysis product (GLOBAL_MULTIYEAR_BGC_001_029) and represent a carbonate-system state variable calculated within the model. The daily pH data were obtained from in situ pH sensor measurements at the KEO mooring. Even though the daily pH and pCO2 measurements are independent in terms of data acquisition, both variables remain constrained by the same carbonate-system thermodynamics. Therefore, we do not further interpret pH as an independent external driver of pCO2.C-11: Figure 2: Difficult to read (somehow fuzzy).
Response: Revised accordingly.
C-12: Figure 3: Difficult to read (somehow fuzzy).
Response: Revised accordingly.
C-13, Line 310: Authors write: ”For example, the ρ value of pH was 0.5969 at Lc = 0; after incorporating the optimal lag of 23 days, ρ increased to 0.7748, with an improvement of approximately 23 %. For MLOTST, ρ was 0.7271 at Lc = 0; after incorporating the optimal lag of 31 days, ρ rose to 0.9205, representing a 21 % improvement.” I don’t understand why pH would directly drive pCO2 (instead of DIC and or TALK); what do we learn here on the processes governing the CO2 cycle and air-sea CO2 fluxes ?
Response: In this study, the term “driver” does not imply that a variable must be independent of other oceanic processes or act as an external forcing. The marine carbonate system is inherently a highly coupled dynamical system, in which pH, DIC, total alkalinity (TALK), and pCO2 are mutually constrained and dynamically linked. L-CCM is used to identify directional causal information within such a coupled dynamical system, rather than to decompose the effects of individual variables into mutually independent physical contributions.
It should also be noted that both TCO₂ and TALK were included among the candidate variables and were likewise identified as having significant causal relationships with pCO2. The relatively high cross-mapping skill of pH reflects its strong causal coupling with pCO2 within the carbonate system, but does not imply that pH is more fundamental than DIC or TALK, nor that pCO2 is controlled by pH alone. Rather, variations in surface-ocean pCO2 should be understood as the combined outcome of temperature, DIC, TALK, biogeochemical processes, and physical transport.
With regard to air–sea CO₂ fluxes, the target of the causal analysis in this study is surface-ocean pCO2, rather than the air–sea CO₂ flux itself. Surface-ocean pCO2 directly affects the direction and magnitude of air–sea CO₂ exchange by controlling the ocean–atmosphere CO₂ partial-pressure difference, whereas the actual flux also depends on atmospheric pCO2, gas-transfer velocity, and CO₂ solubility. Therefore, in the revised manuscript, we avoid interpreting our results as a direct causal attribution of air–sea CO₂ fluxes and instead restrict the interpretation to the identification of dynamical drivers of surface-ocean pCO2 and their associated time lags.C-14, Line 335: Authors write: ”Chl, pH and Vwind showed lower ρ values at the daily-scale (Lc = 0) than at the monthly-scale, which may be attributed to insufficient data volume”. To better understand this description authors should indicate somewhere the number of data used. I think a table with the list of parameters and reference of data-sets is needed.
Response: Revised accordingly.
;;;;;;;;; References added in this review not listed in the MS
Response: Revised accordingly.
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Citation: https://doi.org/10.5194/egusphere-2026-3875-AC1
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AC1: 'Reply on RC1', Min Liu, 11 Oct 2026
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RC2: 'Comment on egusphere-2026-3875', Anonymous Referee #2, 28 Sep 2026
The manuscript adds an explicit causal lag (Lc) to convergent cross mapping (CCM), taking the lag that maximizes cross-map skill as the optimal lag (Lc,opt). The resulting L-CCM is applied to sea surface pCO2 in the subtropical Northwest Pacific in two steps. Standard CCM on monthly regional data (2000–2020) screens 18 candidate drivers, and L-CCM on daily KEO mooring data estimates their lags. The authors report an average 10.32 % increase in causal strength and group the drivers into short-lag, medium-to-long-lag and weakly causal classes. The question is relevant: different controls on pCO2 plausibly act on different effective time scales. Combining a long monthly record with high-frequency mooring data is an attractive design. The variable set is broad, the main drivers identified (e.g. SST, nutrients) are broadly consistent with established understanding, and the paper is generally well organized.
Major comments
1. Scanning cross-map skill over a lag was introduced by Ye et al. (2015) as extended CCM and is available in rEDM/pyEDM through the tp argument. Estimating X(t) from MY(t + Lc) is the non-positive-lag half of that analysis. This work is not cited, so the claim that mainstream CCM ignores lags and the novelty claims need to be revised.
2. fgCO2 is computed from the air–sea pCO2 difference, so it cannot be a driver of pCO2; yet it is listed as one in the Conclusions (L350). pH, TCO2 and TALK are carbonate-system state variables. If they come from a CMEMS product in which pH and DIC are derived from reconstructed pCO2, the highest skill in the study (pH, 0.9467) reflects how the data were constructed rather than causation. Please document the source and derivation of every variable.
3. The 23-day pH lag (L295) is chemically implausible, because pH and pCO2 equilibrate almost instantly, and it rests on only 80 samples (L335). Conversely, signed current and wind components are not the relevant physical forcings; advection (u·∇C) and wind speed or U102 are. Their weak causality therefore says little about the method.
4. Monthly versus daily analysis. The two analyses differ in spatial scale (regional mean vs single point), data sources, period and sample size. The higher daily skills for SSS, Si and TALK (Sect. 3.2.2b) therefore cannot be attributed to temporal resolution, and still less to Lc: for SSS and TALK the L-CCM gain in Fig. 4 is only 0.0% and 0.3%. The related statements (L329–330, L362–363) should be revised. A controlled comparison is needed: CCM versus L-CCM on the same data, and KEO data aggregated to monthly means.
5. As for the daily data, 275 days is about nine months, less than a seasonal cycle, although KEO data exist from 2004 onwards (L104). Please give the period used and extend the record. Please also explain how gaps were handled (275 samples per variable in L109, but only 80 for pH in L335) and how the CMEMS grid points were chosen (L107–108).
6. Comparing ρ in the two directions (L219, L249–251) does not establish a dominant direction; significant skill in both directions indicates bidirectional coupling or synchrony. The SSS result, where the reverse skill is higher, should be read as a warning sign, since pCO2 cannot drive salinity. In Fig. 3 the reverse skill also exceeds the forward skill for Uo, Vo, Uwind and Vwind at most lags. Pairwise CCM also cannot separate direct from indirect effects; for example, SST influences both O2 and pCO2. Partial cross mapping (Leng et al., 2020) could help here.Minor comments
L26–28: pCO2 is the partial pressure of CO2 in a gas phase in equilibrium with the seawater sample, not a "concentration when gas exchange … reaches dynamic equilibrium".
L77: I suggest describing pCO2 as a key state variable linking upper-ocean carbon processes to the air–sea CO2 gradient, rather than as "the core parameter characterizing the ocean carbon sink".
L91–99: SOCAT provides fCO2; please describe the conversion and cite the SOCAT version actually used (Bakker et al., 2016 describes v3, which does not reach 2020). Please also give the CMEMS product IDs and the source of the wind data, and explain how the 4 missing months were handled.
L135–137, L339: the Fig. 3 axes show scan ranges of 30, 40, 60 (MLOTST) and 90 d (Uwind), not 0–30/40 d as stated. Optima at the edge of the scanned range should not be treated as identified.
L144–146, L180, Fig. 2: L denotes both the series length and the library length. Please use separate symbols and describe the library design (sampling scheme, number of realisations, Lmin, Lmax, step). The NO3− panel in Fig. 2 ends at L ≈ 60, which is inconsistent with the 248 samples stated in L99.
Eq. (5): the range should be t ∈ [(E − 1)τ + 1, L − Lc], as in Eq. (6).
L160: "pseudo-nearest-neighbor" presumably means false nearest neighbours (Kennel et al., 1992). L170–173: K = E + 1 follows from the minimal simplex (Sugihara and May, 1990); Agnon et al. (1999) is not an appropriate reference.
L188: "monthly-scale data from 2021" contradicts 2000–2020.
L250: besides SSS, the reverse skill also exceeds the forward skill for Uo and Vgos in Fig. 1.
L255: only 8 of the 18 drivers in Fig. 1 exceed 0.6.
L310–323: please define how the percentages are computed. L323 ("all other drivers also improved") contradicts L333–334.
Fig. 3 vs Fig. 4: at Lc = 0, Fig. 3 appears to show ρ ≈ 0.44 for pH and ≈ 0.79 for MLOTST, whereas the text gives 0.5969 and 0.7271. Please check.
The language needs editing, and claims such as "fully validated", "greatly enhances" and "accurately quantify" should be toned down.Citation: https://doi.org/10.5194/egusphere-2026-3875-RC2 -
AC2: 'Reply on RC2', Min Liu, 11 Oct 2026
We sincerely thank the reviewer for the careful evaluation of our manuscript and for the valuable and constructive comments and suggestions. Our detailed point-by-point responses are provided below.
Major comments
1. Scanning cross-map skill over a lag was introduced by Ye et al. (2015) as extended CCM and is available in rEDM/pyEDM through the tp argument. Estimating X(t) from MY(t + Lc) is the non-positive-lag half of that analysis. This work is not cited, so the claim that mainstream CCM ignores lags and the novelty claims need to be revised.Response: We thank the reviewer for pointing out the important study by Ye et al. (2015) on extended convergent cross mapping. This study provides an important methodological foundation for examining cross-mapping relationships at different time lags. Following the reviewer’s suggestion, we have added a citation to and discussion of this study in the revised manuscript, and further refined the descriptions of the methodological background and the contributions of our work.
In the revised manuscript, we have more clearly explained the relationship between our method and previous studies on lagged cross mapping. We have also clarified that the focus of this study is to systematically investigate cross-mapping relationships at different time lags for multiple potential controlling factors of sea surface pCO₂, identify the optimal lag Lc,opt based on the maximum cross-mapping skill, and establish a two-stage analytical framework that combines long-term monthly-scale data with daily-scale data to identify potential drivers and characterize their temporal lag features.
The relevant content has been supplemented and revised in the Introduction and Methods sections.2. fgCO2 is computed from the air–sea pCO2 difference, so it cannot be a driver of pCO2; yet it is listed as one in the Conclusions (L350). pH, TCO2 and TALK are carbonate-system state variables. If they come from a CMEMS product in which pH and DIC are derived from reconstructed pCO2, the highest skill in the study (pH, 0.9467) reflects how the data were constructed rather than causation. Please document the source and derivation of every variable.
Response: The L-CCM method used in this study was developed by incorporating a time-lag parameter into the state-space reconstruction and cross-mapping framework of CCM, while retaining the same fundamental principle of causal inference. CCM is designed to identify causal relationships between variables in coupled nonlinear dynamical systems, and its application does not require the variables under investigation to be independent of one another. However, in systems characterized by complex coupling relationships, high cross-mapping skill should be interpreted as evidence of a causal connection between variables, rather than as sufficient proof that one variable exerts an independent, direct causal effect on another. Therefore, in this study, cross-mapping skill and its convergence characteristics are retained as important criteria for evaluating potential causal coupling relationships between variables, with the interpretation of the results also taking into account the physical and chemical properties of the variables and relevant data characteristics.
Regarding FgCO₂, as a measure of air–sea CO₂ exchange flux, it is directly related to the air–sea pCO₂ gradient and gas exchange processes. Accordingly, in the revised manuscript, we have further clarified the diagnostic nature of FgCO₂ and adjusted the relevant statements in the conclusions to distinguish it from environmental controlling variables such as temperature and nutrients. For carbonate-system variables such as pH, TCO₂, and TALK, their high cross-mapping skill may reflect their close coupling with pCO₂ within the carbonate system. Meanwhile, considering that these variables are derived from the same carbonate-system product and that dependencies may exist between some variables as a result of the product construction process, we have further interpreted the relevant results in light of the physicochemical properties of the variables and the characteristics of the product generation process. More detailed information on the data sources has been added to the revised manuscript, and the interpretation of the relevant results has been refined accordingly.3. The 23-day pH lag (L295) is chemically implausible, because pH and pCO2 equilibrate almost instantly, and it rests on only 80 samples (L335). Conversely, signed current and wind components are not the relevant physical forcings; advection (u·∇C) and wind speed or U102 are. Their weak causality therefore says little about the method.
Response: Within the L-CCM framework, the optimal lag Lc,opt represents the temporal scale at which the maximum cross-mapping skill is achieved under different temporal offsets. It reflects the lagged coupling between two observed time series rather than the characteristic response time of an individual chemical reaction. In the revised manuscript, we have adjusted the description of this result accordingly to avoid overinterpreting the 23-day lag in terms of specific chemical mechanisms.
The daily pH data were obtained from in situ observations at the KEO mooring station. However, because the observation record contains frequent temporal gaps, the longest effective sequence available for continuous lag analysis consists of 80 samples. Consequently, compared with variables with longer continuous records, the estimation of the pH lag is subject to limitations imposed by the sample length, as already noted in Section 3.2.3 of the original manuscript.
The zonal and meridional components were selected primarily because they are commonly used fundamental representations of ocean circulation and wind fields and are directly provided by the data products used in this study. The purpose of variable selection was not to exhaust all possible representations of the underlying dynamics, but rather to select a representative set of environmental variables with good data availability for analysis. We acknowledge that current speed, flow direction, and wind speed can provide complementary information on the relevant dynamics. Nevertheless, the component variables used in this study have clear physical meanings and can characterize dynamical variations in different directions.4. Monthly versus daily analysis. The two analyses differ in spatial scale (regional mean vs single point), data sources, period and sample size. The higher daily skills for SSS, Si and TALK (Sect. 3.2.2b) therefore cannot be attributed to temporal resolution, and still less to Lc: for SSS and TALK the L-CCM gain in Fig. 4 is only 0.0% and 0.3%. The related statements (L329–330, L362–363) should be revised. A controlled comparison is needed: CCM versus L-CCM on the same data, and KEO data aggregated to monthly means.
Response: We recognize that the original manuscript did not clearly distinguish the purposes of the comparisons between monthly-scale CCM and daily-scale L-CCM, which may have led to misunderstandings. We have therefore revised the relevant descriptions and provide further clarification here.In fact, this study involves two comparisons with distinct purposes. First, the monthly-scale CCM analysis based on multi-year data is primarily intended to identify relatively stable long-term patterns of causal relationships in the study region. These results serve as a reference for the daily-scale L-CCM results, allowing us to assess whether the main identified causal relationships remain broadly consistent. The comparison between monthly-scale CCM and daily-scale L-CCM is not intended to quantitatively evaluate the performance improvement of L-CCM. Differences observed for some variables between the two analyses have been discussed in Sect. 3.2.3.
The comparison used to evaluate the improvement achieved by L-CCM is instead conducted within the same daily-scale dataset. Within the L-CCM framework, when Lc=0, the model reduces to the CCM case without considering a causal lag. When Lc is searched over a specified range, the optimal causal lag, Lc,opt, corresponding to the maximum cross-mapping skill can be identified. Accordingly, this study compares the cross-mapping skill at Lc=0 and Lc=Lc,opt under identical conditions, including the same variables, data sources, spatial locations, study period, and sample conditions. In Fig. 4, ρ1 represents the result at Lc=0, whereas ρ2 represents the maximum cross-mapping skill at Lc=Lc,opt. The improvement percentages reported in the manuscript are derived from this controlled within-dataset comparison, rather than from a direct comparison between the monthly-scale and daily-scale results.5. As for the daily data, 275 days is about nine months, less than a seasonal cycle, although KEO data exist from 2004 onwards (L104). Please give the period used and extend the record. Please also explain how gaps were handled (275 samples per variable in L109, but only 80 for pH in L335) and how the CMEMS grid points were chosen (L107–108).
Response: The daily-scale data used in this study were initially obtained for the entire year. However, because different observational datasets and data products contained varying degrees of missing data and temporal discontinuities during the study period, and because the time-lag analysis in L-CCM relies on continuous time series, we selected the longest continuous period from the commonly available valid data for analysis. For most variables, we ultimately used continuous daily time series from 1 April to 31 December 2019. Because the pH observations during this period contained substantial missing data and temporal discontinuities, it was not possible to obtain a continuous record of the same length as those of the other variables. Therefore, we used the longest continuous valid time series for pH, spanning 27 September to 14 December 2019. Considering its relatively short sample length, we have explicitly acknowledged this limitation in the revised manuscript and adopted a more cautious interpretation of the corresponding lag results.
For environmental variables not provided by KEO, we extracted gridded data corresponding to the KEO location from the relevant Copernicus Marine daily products and temporally matched them with the KEO observations based on common dates to construct continuous time series.6. Comparing ρ in the two directions (L219, L249–251) does not establish a dominant direction; significant skill in both directions indicates bidirectional coupling or synchrony. The SSS result, where the reverse skill is higher, should be read as a warning sign, since pCO2 cannot drive salinity. In Fig. 3 the reverse skill also exceeds the forward skill for Uo, Vo, Uwind and Vwind at most lags. Pairwise CCM also cannot separate direct from indirect effects; for example, SST influences both O2 and pCO2. Partial cross mapping (Leng et al., 2020) could help here.
Response: CCM is a nonlinear causal inference method based on state-space reconstruction. The L-CCM method proposed in this study retains the fundamental principles of causal inference underlying CCM. Therefore, we continue to interpret the relationships identified by CCM/L-CCM as causal relationships. In this study, causal direction is not determined solely on the basis of forward and reverse cross-mapping skills obtained from daily-scale data for a single year. The multi-year monthly-scale CCM analysis also serves as a reference for interpreting causal relationships in the study region. For example, Uwind exhibits higher reverse than forward cross-mapping skill in the daily-scale analysis, whereas the forward relationship is more pronounced in the long-term monthly-scale CCM analysis. Therefore, we interpret the results by considering both the monthly-scale CCM and daily-scale L-CCM analyses. For variables whose inferred causal directions are not fully consistent between the two analyses, we do not directly interpret the magnitude of (\rho) from the daily-scale analysis alone as evidence of a stable, long-term unidirectional causal effect. For variables such as SSS, which also exhibit relatively high reverse cross-mapping skills, we have further revised the relevant statements in the revised manuscript.
CCM/L-CCM analysis can identify causal relationships between two variables, but it cannot, by itself, strictly distinguish whether a causal influence arises through a direct pathway or is transmitted indirectly through other variables in the system. It is also difficult to completely exclude the influence of common drivers. In strongly coupled multivariate dynamical systems, rigorously distinguishing direct from indirect causal pathways remains challenging. Multivariate approaches, such as partial cross mapping, may provide complementary information for further resolving complex causal pathways. However, such analyses are beyond the scope of the current research framework and will be considered as a direction for future research.Minor comments
L26–28: pCO2 is the partial pressure of CO2 in a gas phase in equilibrium with the seawater sample, not a "concentration when gas exchange … reaches dynamic equilibrium".Response: Completed.
L77: I suggest describing pCO2 as a key state variable linking upper-ocean carbon processes to the air–sea CO2 gradient, rather than as "the core parameter characterizing the ocean carbon sink".
Response: Completed.
L91–99: SOCAT provides fCO2; please describe the conversion and cite the SOCAT version actually used (Bakker et al., 2016 describes v3, which does not reach 2020). Please also give the CMEMS product IDs and the source of the wind data, and explain how the 4 missing months were handled.
Response: This study used SOCAT v2023 data covering the period from 2000 to 2020. We converted fCO₂ to pCO₂ using the corresponding temperature-dependent conversion relationship. After spatially and temporally matching sea surface pCO₂ with the environmental variables, four months during 2000–2020 lacked complete sets of commonly valid records: February 2004, February 2005, July 2005, and March 2006. These four months were therefore excluded from the subsequent CCM analysis, resulting in a final dataset of 248 monthly samples.
In the revised manuscript, we have added the conversion formula and relevant references, explicitly specified the SOCAT version used in this study, and included a new table detailing the data sources.L135–137, L339: the Fig. 3 axes show scan ranges of 30, 40, 60 (MLOTST) and 90 d (Uwind), not 0–30/40 d as stated. Optima at the edge of the scanned range should not be treated as identified.
Response：In the actual analysis, most variables exhibited relatively clear changes in ρ within the lag range of Lc=30–40 d. Specifically, the cross-mapping skill gradually decreased after reaching its peak and tended to stabilize over the subsequent lag range. Therefore, this search range was considered sufficient to cover the main response interval for most variables.
For MLOTST and Uwind, however, the ρ–Lc curves did not exhibit similarly clear post-peak declines and stabilization within the conventional search range of 30–40 d, suggesting that the maximum cross-mapping skill might occur at larger lags. To reduce the possibility of truncating a potential peak due to an insufficiently large upper search limit and to improve the reliability of optimal lag identification, we appropriately extended the search ranges for these two variables.L144–146, L180, Fig. 2: L denotes both the series length and the library length. Please use separate symbols and describe the library design (sampling scheme, number of realisations, Lmin, Lmax, step). The NO3− panel in Fig. 2 ends at L ≈ 60, which is inconsistent with the 248 samples stated in L99.
Response: We have standardized and corrected the relevant notation, using N to denote the total number of samples in the time series and L to denote the library size in the CCM analysis. The total number of monthly samples used in this study is N=248. In addition, we have provided further details on the library size settings and the corresponding computational procedures in the Methods section of the revised manuscript.The results presented in Fig. 2 were incomplete. We have therefore redrawn the figure and revised the corresponding descriptions accordingly.
Eq. (5): the range should be t ∈ [(E − 1)τ + 1, L − Lc], as in Eq. (6).
Response: Completed.
L160: "pseudo-nearest-neighbor" presumably means false nearest neighbours (Kennel et al., 1992). L170–173: K = E + 1 follows from the minimal simplex (Sugihara and May, 1990); Agnon et al. (1999) is not an appropriate reference.
Response: Yes, the term “pseudo-nearest-neighbor” used in the original manuscript was inaccurate. The method actually referred to is the false nearest neighbors (FNN) method. We have therefore corrected the terminology and added a reference to Kennel et al. (1992). The citation to Agnon et al. (1999) has also been removed.
L188: "monthly-scale data from 2021" contradicts 2000–2020.
Response: Thank you for pointing this out. The phrase “from 2021” in the original manuscript was a typographical error. The correct expression should be “from 2000 to 2020”, covering a total of 21 years. We have corrected this error in the revised manuscript.
L250: besides SSS, the reverse skill also exceeds the forward skill for Uo and Vgos in Fig. 1.
Response: Fig. 1 shows that, in addition to SSS, the reverse cross-mapping skills of Uo and Vgos are also numerically higher than their corresponding forward cross-mapping skills. However, the \(\rho\) values for Uo and Vgos are generally low in both directions (all below approximately 0.13), indicating only weak or indistinct causal relationships with pCO₂. In contrast, for variables exhibiting relatively high cross-mapping skills, differences between the forward and reverse results have clearer interpretative significance. We have revised the relevant statements in the main text accordingly.
L255: only 8 of the 18 drivers in Fig. 1 exceed 0.6.
Response: Yes, the wording in the original manuscript was not sufficiently accurate. We have revised the relevant statements accordingly.
L310–323: please define how the percentages are computed. L323 ("all other drivers also improved") contradicts L333–334.
Response: Completed.
Fig. 3 vs Fig. 4: at Lc = 0, Fig. 3 appears to show ρ ≈ 0.44 for pH and ≈ 0.79 for MLOTST, whereas the text gives 0.5969 and 0.7271. Please check.
Response: Completed.
The language needs editing, and claims such as "fully validated", "greatly enhances" and "accurately quantify" should be toned down.
Response: Completed.
Citation: https://doi.org/10.5194/egusphere-2026-3875-AC2
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AC2: 'Reply on RC2', Min Liu, 11 Oct 2026
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;;;;;;;;;; General comment
In this manuscript authors present methods (CMM and L-CMM) to investigate the drivers of the oceanic surface pCO2. This is applied in the North-West Pacific subtropical region using SOCAT and CMES data-sets for the period 2000 to 2020. Authors conclude that “SST, Si, PO43-, O2, TCO2 and TALK serve as core dominant drivers of pCO2 variation”. I guess such result is known since decades (e.g. Takahashi et al 1993, 2002). What is new here and how this helps interpreting the processes that drive the ocean CO2 cycle (and air-sea CO2 fluxes) ? As the results confirm many previous studies and because authors have in hand the global SOCAT data-set, I suggest the authors extend their analysis to the global ocean, e.g. applying the methods to all biomes (Fay and McKinley, 2014)
In its present form the paper is not suitable for publication and need major revision. Figures need to be revised and I think some figures are missing. A list of the data-sets used should be presented in a table with associated references. I’ve listed below specific comments and questions.
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C-01, Line 24: Authors write: ”Against the backdrop of global climate change, the ocean, as one of the largest active carbon sinks, plays a critical buffering role in the climate system by regulating atmospheric CO₂ concentrations (Tjiputra et al., 2025)”. Is Tjiputra et al., (2025) who used models relevant reference for this note. I think Friedlingstein et al, (2025) should also be refer.
C-02: Section “2.1.1 Overview of the Study Area”. A map of the region with a scheme of circulation would be useful for readers not familiar with this region. Such map could include the mean air-sea CO2 fluxes as color code.
C-03, Line 73: Authors write: ”We focused on the subtropical waters of the northwestern Pacific (28° N–40° N, 140° E–180° E). As one of the world’s major ocean carbon sinks(Chen et al., 2025), this region exhibits substantial air-sea CO₂ exchange fluxes and is shaped by complex ocean dynamic processes, making it an ideal study area for identifying causal relationships among key components and driving factors of the ocean carbon sink.” Why focusing in the NW SBT Pacific ? In this region, it is well known that pCO2 is mainly driven by SST (e.g. Inoue et al, 1999; Takahashi et al, 2002). I think authors should list previous studies and processes identified and quantified) as main drivers of pCO2 at seasonal to multi-decadal scales.
C-04, Line 77: Authors write: ”We selected sea surface partial pressure of carbon dioxide (pCO₂) as the core parameter characterizing the ocean carbon sink, and identified its potential driving factors”. Please, explain why you prefer to select pCO2 rather than DIC that is a core parameter of the CO2 cycle (recall that pCO2 is the result of DIC, ALK and SST).
C-05, Line 79: Why pH is listed in the driven variables ?
C-06, Line 91: Authors write: ”The sea surface pCO₂ observations were retrieved from the Surface Ocean CO₂ Atlas (SOCAT) (Bakker et al., 2016). ” Please specify the SOCAT version and present a map of the SOCAT data you used. Specify the SOCAT data selected (both Cruises and fCO2 flags). As SOCAT data are for fCO2, did you convert the data to pCO2 ?
C-07, Line 98: Authors write: ”The data spanned from 2000 to 2020 at a monthly resolution”. Why this period is selected ? Because of available data ? Other reasons (e.g. Post 1998 ENSO ?).
C-08, Line 100: (b) Daily-scale Data. Original SOCAT data are also at local/daily scales. Why not using the original SOCAT data to get high frequency scale.
C-09: Figure 1 Caption: Sentences repeated.
C-10, Line 214: Authors write: ”Among these, pH and SST exhibited the highest cross-mapping skill with pCO₂, with ρ values reaching 0.9467 (pCO₂ xmap pH) and 0.8064 (pCO₂ xmap SST), respectively, indicating a tight coupling relationship between these factors and pCO₂”. I probably understand the high skill for SST in the SBT region but I don’t understand the link with pH. By the way, what are the pH data used ? I guess this is not clearly listed in the manuscript. Are the pH data independent from pCO2 ? Is it measured or calculated pH ?
C-11: Figure 2: Difficult to read (somehow fuzzy).
C-12: Figure 3: Difficult to read (somehow fuzzy).
C-13, Line 310: Authors write: ”For example, the ρ value of pH was 0.5969 at Lc = 0; after incorporating the optimal lag of 23 days, ρ increased to 0.7748, with an improvement of approximately 23 %. For MLOTST, ρ was 0.7271 at Lc = 0; after incorporating the optimal lag of 31 days, ρ rose to 0.9205, representing a 21 % improvement.” I don’t understand why pH would directly drive pCO2 (instead of DIC and or TALK); what do we learn here on the processes governing the CO2 cycle and air-sea CO2 fluxes ?
C-14, Line 335: Authors write: ”Chl, pH and Vwind showed lower ρ values at the daily-scale (Lc = 0) than at the monthly-scale, which may be attributed to insufficient data volume”. To better understand this description authors should indicate somewhere the number of data used. I think a table with the list of parameters and reference of data-sets is needed.
;;;;;;;;; References added in this review not listed in the MS
Fay, A. R., and McKinley, G. A.: Global open-ocean biomes: Mean and temporal variability. Earth System Science Data, 6(2), 273–284. https://doi.org/10.5194/essd-6-273-2014, 2014
Friedlingstein, P., et al: Global Carbon Budget 2024, Earth Syst. Sci. Data, 17, 965–1039, https://doi.org/10.5194/essd-17-965-2025, 2025.
Inoue, H.Y., Ishii, M., Matsueda, H., Saito, S., Midorikawa, T. and Nemoto, K. (1999) ‘MRI measurements of partial pressure of CO2 in surface waters of the Pacific during 1968 to 1970: re-evaluation and comparison of data with those of the 1980s and 1990s’, Tellus B: Chemical and Physical Meteorology, 51(4), p. 830–848. Available at: https://doi.org/10.3402/tellusb.v51i4.16492.
Takahashi, T., Olafsson, J., Goddard, J. G., Chipman, D. W., and Sutherland, S. C.: Seasonal variation of CO2 and nutrients in the high-latitude surface oceans: A comparative study, Global Biogeochem. Cycles, 7, 843–878, https://doi.org/10.1029/93GB02263, 1993.
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