Sea surface CO2 fugacity (fCO2(sw)) data, along with ancillary variables, were obtained from the Surface Ocean CO2 Atlas (SOCAT; Pfeil et al., 2013; Bakker et al., 2016) version 2021 (SOCATv2021) for latitudes between 15 and 60∘ N and longitudes between 105 and 140∘ W (hereafter referred to as “the study region”). SOCAT is an international effort to synthesize quality-controlled fCO2(sw) observations for the global surface ocean, and has released datasets of individual surface ocean fCO2(sw) observations and gridded values since 2011, with annual releases since 2015. SOCATv2021 contains nearly 30.6 million fCO2(sw) observations globally and over 1.4 million fCO2(sw) observations within the study region.

SOCAT data in the study region were filtered to retain fCO2(sw) observations with a measurement quality control (QC) flag of 2 (“good”) and dataset QC flags of A through D (fCO2(sw) accuracy of 5 µatm or better). This is identical to the QC procedure followed by the SOCAT team for producing gridded data products (Sabine et al., 2013; Bakker et al., 2016). SOCATv2021 provides ancillary variables along with fCO2(sw), including contemporaneous observations of sea surface temperature (SST) and sea surface salinity (SSS), as well as atmospheric pressure at the ocean surface (Patm) from the National Centers for Environmental Prediction (NCEP) reanalysis; these values were used only for fugacity to partial pressure conversions (Eq. 1). Though SST and SSS are considered surface values, it is important to note that these are primarily underway measurements taken a few meters beneath the surface and that nontrivial differences in temperature and salinity may exist between the measurement depth and the surface (Robertson and Watson, 1992; Donlon et al., 2002; Goddijn-Murphy et al., 2015; Woolf et al., 2016; Ho and Schanze, 2020; Watson et al., 2020). Also, while SST and SSS are not assigned explicit QC flags in SOCAT, these parameters do undergo quality control checks during the calculation of fCO2(sw) (Lauvset et al., 2018).

Sea surface CO2 fugacity represents CO2 partial pressure corrected for the nonideality of CO2 gas. It was converted to sea surface CO2 partial pressure (pCO2(sw)) following (Weiss, 1974) 1pCO2(sw)=fCO2(sw)⋅exp⁡PatmB+2⋅δR⋅T-1, where B and δ are virial coefficients, R is the ideal gas constant, and T is SST in Kelvin.

Sea surface CO2 partial pressure data were aggregated onto a 0.25∘ latitude by 0.25∘ longitude grid for each month from January 1998 to December 2020 using a bin-averaging procedure that consisted of computing the means (μ) and standard deviations (σ) of all observations of pCO2(sw) included within each grid cell. Observations prior to 1998 were excluded as an increase in fCO2(sw) data coverage occurs around the start of 1998 and the first full year of SeaWiFS chlorophyll observations (which are used in our procedure to fill gaps in the pCO2(sw) dataset) is 1998. For cases in which observations in a given grid cell originated from two or more platforms (e.g., cruises or autonomous assets), platform-weighted μ and σ were computed by first taking the means and standard deviations of all observations made by each platform, then taking the means of those values. This ensured that all platforms contributing observations to a given grid cell were weighted equally, mitigating unwanted biases toward high-resolution measurement systems (Sabine et al., 2013).

This bin-averaging procedure is identical to the one followed by the SOCAT team for producing monthly datasets for coastal regions with 0.25∘ resolution as well as for open-ocean regions with 1∘ resolution (Sabine et al., 2013; Bakker et al., 2016). However, here we produced a monthly gridded dataset with 0.25∘ resolution for a region of the northeastern Pacific (15 to 60∘ N, 105 to 140∘ W) that spans both the coastal and open ocean. Means of pCO2(sw) from this gridded dataset (averages over the monthly climatology from 1998 to 2020 for each spatial grid cell) are shown in Fig. 1. Some of the apparent fine-scale spatial variability in this bin-averaged map is not indicative of true environmental conditions but originates from the combination of large temporal variability within each grid cell and uneven sampling of each grid cell across and within years. This form of temporal variability is exactly the kind of spurious result that advanced pCO2(sw) mapping techniques are intended to circumvent. Figure B1 shows the number of years containing an observation within each month of our gridded pCO2(sw) dataset. Unsurprisingly, temporal coverage is highest close to the coast, especially in the summer months.

Of the 4 014 844 grid cells that represent the surface ocean gridded in three dimensions at 0.25∘ resolution over 276 months (1998–2020) in the study region, just 1.25 % have an associated gridded pCO2(sw) value. To fill gaps in this dataset, relationships between pCO2(sw) and various predictor variables need to be determined. The predictor variables used in this study are primarily derived from satellite observations or reanalysis models due to the condition that they be resolved with temporal and spatial continuity across the study region and selected time span.

Predictor variables are intended to capture conditions that mechanistically influence pCO2(sw) (e.g., SST and atmospheric pCO2), serve as a proxy for mechanisms that influence pCO2(sw) (e.g., sea surface chlorophyll), or, in the case of temporal and spatial information, constrain additional patterned variability not captured by the mechanistic variables alone. The chosen predictor variables for this study (Table 1) have all been used before for pCO2(sw) gap-filling methods (e.g., Landschützer et al., 2014; Gregor et al., 2018; Denvil-Sommer et al., 2019; Watson et al., 2020); temporal and spatial predictors were included to ensure robust representation of pCO2(sw) seasonal cycles (Gregor et al., 2017). Included in Table 1 are the sources of each dataset, the original resolutions of each dataset, and the steps that were taken to process each dataset. Appendix A provides more detail about the acquisition and processing of the driver variables and includes figures showing annual means of selected variables.

We used the random forest regression approach (Breiman, 2001) to identify relationships between pCO2(sw) and predictor variables in order to fill gaps in the gridded pCO2(sw) dataset. This method averages the results from a number of decision and/or regression trees (i.e., a “forest”) built on bootstrapped replicates of the dataset – which individually have low bias and high variance – to produce a final regression model with reduced variance (Hastie et al., 2009). RFR is the machine-learning method of choice for this study as early testing showed better performance than the SOM-FNN method in the northeastern Pacific. Further, RFR is less computationally expensive than fitting a neural network and has been shown to produce results comparable to the SOM-FFN approach in terms of overall performance (Gregor et al., 2017). It should be noted, however, that the two approaches differ mechanistically and therefore adapt to variability within a training dataset in different ways. Finally, while RFR has been explored more frequently in recent years as a method of spatiotemporal pCO2(sw) gap-filling both globally (Gregor et al., 2017, 2018) and regionally in the Gulf of Mexico (Chen et al., 2019), far fewer RFR-based pCO2(sw) products exist than neural-network-based products. So, this study provides a good opportunity to further demonstrate the utility of RFR for producing monthly fields of pCO2(sw), in this case on a regional scale in the northeastern Pacific.

Each decision tree within a random forest regression model is built on a different subset of the training dataset (that contains both the predictor variables and corresponding gridded pCO2(sw) values). This subset is generated by bootstrapping, in which a random set of training data points is selected with replacement – meaning the same data point can be selected more than once (Breiman, 1996). The number of data points in the bootstrapped dataset is equal to a defined fraction (InBagFraction in Table 2) of the original dataset; however, a fraction equal to 1 does not mean the bootstrapped dataset is identical to the original dataset because selection is made with replacement. Since each regression tree is built on a different subset of the training data, it will contain somewhat different relationships between the predictor variables and the corresponding gridded pCO2(sw) values.

The process of building a decision tree begins at the top “node” of the tree with the values of a single predictor variable being used to split that tree's bootstrapped subset of the training dataset into two smaller subsets (not necessarily of equal size) containing the most similar pCO2(sw) observations (i.e., sets of pCO2(sw) observations with the smallest variance among them). These subsets are then further divided into progressively smaller sets of similar observations until either the variance among the pCO2(sw) observations in a node drops below a prescribed tolerance level or the number of observations in the node reaches the user-defined minimum (MinLeafSize in Table 2). To ensure that the algorithm does not always pick the same predictor variable (e.g., the one most highly correlated with pCO2(sw) overall) for the split at every node, we limit it to choosing from a different random subset of the predictor variables (equal in number to NumPredictorsToSample in Table 2) at each node. This introduces another “random” element into the tree-building process. The random forest contains a large number of these regression trees (NumTrees in Table 2) each built on a different, random bootstrapped subsample of the training data. Once the random forest is built, a set of predictor variables can be provided to the model and the average of the pCO2(sw) values provided by each regression tree is used as the pCO2(sw) prediction for that particular set of inputs.

We constructed an RFR model using the MATLAB TreeBagger function with the predictor variables given in Table 1 and the parameters given in Table 2, along with gridded pCO2(sw) values that were obtained as described in Sect. 2.1 and 2.2. To produce the northeastern Pacific random forest regressionpCO2(sw) product (RFR-CCS) that is the main result of this work (Sharp et al., 2022; 10.5281/zenodo.5523389), the full dataset of gridded pCO2(sw) values was used. For optimization and evaluation, subsets of the full dataset were used as described in the following sections.

The predictor variables used (Table 1) and the values for the model parameters (Table 2) were determined by iteratively optimizing the model performance. First, default model parameters were used to train an RFR model using a subset of the data for training (80 % of full dataset, distributed randomly across the space and time domains of interest) and a number of possible predictor variables: latitude, longitude, sea surface height, bottom depth, and those given in Table 1. During model selection, the generalization skill for the RFR model was assessed using a validation dataset comprised of 10 % of the full dataset, none of which was included in the training data. After the initial model fit, predictors with a “feature importance” (computed during the RFR fit) significantly lower than all other predictors were sequentially dropped (latitude, longitude, and sea surface height), and this did not substantially change the training or validation root mean squared error (RMSE). Remaining predictor variables were dropped one at a time for subsequent fits, and the goodness-of-fit and generalization skill of the model were assessed using the RMSE values calculated from applying the model to the training and validation datasets, respectively. The set of predictors with the lowest RMSE after dropping one predictor was carried into the next iteration. If removing a predictor did not increase the validation RMSE significantly, then that predictor was removed from the set of predictors (only bottom depth was dropped in this step). The final set of predictor variables is shown in Table 1.

Next, different values for model parameters (Table 2) were tried iteratively with the retained predictors to identify the optimal values, again by minimizing the RMSE of the validation dataset. Although lower values for the minimum terminal node size performed better in this analysis, additional testing indicated that retaining the default value of 5 was important to prevent overfitting. To determine the appropriate number of trees, we examined how the out-of-bag mean squared error changed as more and more trees were included in the random forest (up to 5000 trees) and selected a number of trees well past the point at which this error had stabilized (1200 trees). Finally, the remaining 10 % of the full dataset that was withheld from both the model training and model validation (i.e., the “test data”) was used to quantify the mapping uncertainties from the RFR approach (discussed further in Sects. 2.7 and 3.5). The predictor variable feature importances for the final RFR-CCS fit are given in Fig. B2.

Once predictor variables and model parameters were optimized, the skill of the RFR approach was further evaluated by splitting the full dataset into different subsets of training data and test data. Evaluation models (RFR-CCS-Evals) were constructed in three different ways: (1) by removing a random (20 %) subset of cruises and/or measurement platforms from the training data (repeated 10 times with different subsets removed each time; n=10), (2) by removing all observations from every fifth year from the training data (repeated five times such that data from every year was removed from one of the trials; n=5), and (3) by removing all moored autonomous pCO2(sw) measurements (i.e., discrete time series sites primarily located in the coastal ocean) from the training data (n=1). The first two strategies were relevant for assessing bulk error statistics for the method applied across the region and the third strategy for evaluating the ability of the RFR to represent local seasonal variability without the use of high-temporal-resolution mooring data. These RFR-CCS-Evals are distinct model variants that are only used for assessment; the final RFR-CCS model uses all available training data.

Each data split for an RFR-CCS-Eval was applied directly to SOCATv2021 observations, before bin-averaging the data according to the procedure given in Sect. 2.2; as a result, a gridded training dataset and a gridded test dataset were produced from each split. Data splits were performed in this way to ensure that autocorrelation among measurements from a specific platform did not bias the error statistics. Each split was repeated n times, and error statistics (bias, RMSE, and R2) from comparing pCO2(sw) predicted from the RFR-CCS-Eval models versus pCO2(sw) from the gridded test dataset were averaged.

The final RFR-CCS data product was evaluated through comparisons with gridded pCO2(sw) observations from SOCATv4 (Bakker et al., 2016) and pCO2(sw) observations from surface ocean moorings (Sutton et al., 2019). Of the surface ocean moorings within the study site that are not located within an inland sea and have available data from all 12 months of the year, four (CCE2, NH10, Cape Elizabeth, Châ bá) are located within 40 km of shore and one (CCE1) is about 215 km from shore. RFR-CCS was also compared to global-scale gap-filled pCO2(sw) products that are available in the region. Namely, we focused on the coastal multi-month pCO2(sw) product from Laruelle et al. (2017; i.e., L17) and the combined coastal and open-ocean pCO2(sw) climatology from Landschützer et al. (2020b; i.e., L20).

Uncertainty in pCO2(sw) for each grid cell was calculated according to the approach used by Landschützer et al. (2014, 2018) and Roobaert et al. (2019), in which total uncertainty in pCO2(sw) results from a combination of observational uncertainty, mapping uncertainty, and gridding uncertainty. Observational uncertainty (θobs) is uncertainty inherent to the original measurements of pCO2(sw) evaluated as the average of reported uncertainties in the fCO2(sw) observations from our training dataset, which are flagged by SOCAT with a dataset QC flag of A or B (fCO2(sw) accuracy of 2 µatm or better) and of C or D (fCO2(sw) accuracy of 5 µatm or better); we weighted θobs by the number of observations assigned each flag. Mapping uncertainty (θmap) is uncertainty contributed by the RFR mapping procedure and was evaluated as separate values for the coastal (< 400 km from shore) and open ocean (> 400 km from shore) using the mean of the root mean squared errors for a subset of test data (10 %) withheld from both the model training data (80 %) and model validation data (10 %) (see Sect. 2.5). Gridding uncertainty (θgrid) is uncertainty attributable to aggregating observations into monthly 0.25∘ resolution grid cells and was evaluated as separate values for the coastal and open ocean by taking the average unweighted standard deviation among pCO2(sw) values within each grid cell in which two or more platforms were represented. Grid cells with mooring observations were excluded from the θgrid calculation to avoid the high number of observations swamping the signal from other platforms. These three components were combined to obtain total pCO2(sw) uncertainty (θpCO2) applicable to each open-ocean grid cell and to each coastal grid cell: 2θpCO2=θobs2+θmap2+θgrid2. Whereas θpCO2 represents the uncertainty in pCO2(sw) for a given grid cell in a given month, uncertainty averaged regionally or over time will not scale exactly with θpCO2 due to the spatial correlation of pCO2(sw) values and the autocorrelation features of the model error (e.g., Landschützer et al., 2014).

The flux of CO2 across the ocean–atmosphere interface (FCO2) was calculated using a bulk formula: 3FCO2=kw×K0×ΔpCO2, where kw is the gas transfer velocity, K0 is the CO2 solubility constant, and ΔpCO2 is the difference between CO2 partial pressure in seawater and in the overlying atmosphere (pCO2(sw)-pCO2(atm)) The salinity- and temperature-dependent equations of Weiss (1974) were used to calculate K0.

Gas transfer velocities were parameterized using a quadratic dependence on wind speed (Wanninkhof, 1992): 4kw=Γ660⋅U2⋅660/Sc, where Γ660 is a gas exchange coefficient normalized to Sc = 660, U2 is the squared wind speed, and Sc is the Schmidt number for CO2. Our calculations used Γ660=0.276, which is a gas exchange coefficient that is specific to ERA5 reanalysis winds and scaled to a bomb-14C flux estimate of 16.5 cm h-1 (Fay et al., 2021). Sc was calculated using the fourth-order polynomial fit of Wanninkhof (2014). U was obtained from ERA5 reanalysis (Hersbach et al., 2020). Flux calculations used monthly averages of squared 3-hourly wind speeds to retain the influence of the quadratic wind term (Fay et al., 2021).

As described in Sect. 2.6, training and test datasets were created by splitting the full dataset prior to bin-averaging. Evaluation models (RFR-CCS-Evals) were constructed by fitting RFR models using the various gridded training datasets. Values of pCO2(sw) predicted by RFR-CCS-Evals were compared to corresponding values from gridded test datasets. Error statistics (bias, RMSE, and R2) averaged over the n sets of evaluation tests are given in Table 3. When RFR-CCS is compared against all the gridded observations used to construct it, error statistics are predictably strong (last row in Table 3), with a mean bias of 0.00 µatm and an RMSE of 13.33 µatm (R2=0.93). These error statistics demonstrate the ability of the RFR model to fit the training data; the evaluation tests provide insight into the model's ability to predict independent data.

Tests 1 and 2 are good indicators of the overall skill of RFR-CCS. The mean absolute bias for each of those tests is less than 2 µatm, and the RMSEs are near or below 30 µatm. These error statistics can be compared with those of L17, who obtained biases with a mean of 0.0 and RMSEs ranging from 20.5 to 53.1 µatm (mean of 39.2 µatm) for independent evaluations of coastal pCO2(sw) values fit using the SOM-FFN method in 10 separate global subregions at 0.25∘ resolution. For an open-ocean comparison, Denvil-Sommer et al. (2019) obtained an RMSE of 15.86 for an independent evaluation of pCO2(sw) values fit using a similar neural network approach (LSCE-FFNN) for the subtropical North Pacific (18 to 49∘ N) at 1∘ resolution. The error statistics for our study region, which spans the coastal to open-ocean continuum on a finely resolved spatial grid, lie comfortably between those coastal and open-ocean comparison points.

Test 3 is a good indicator of how well the RFR approach is able to reproduce the values and seasonalities of coastal pCO2(sw) at fixed locations when mooring data at a given location are not provided as training data, as each of the moorings makes continuous pCO2(sw) measurements throughout the year and all but one of the mooring locations included in SOCATv2021 in this region are within 40 km of shore. The positive mean bias (8.39 µatm) suggests that RFR-CCS somewhat overestimates pCO2(sw) at grid cells corresponding to mooring locations, but this is strongly influenced by high biases at the Cape Elizabeth and Châ bá mooring locations (Table B1). The relatively high RMSE (43.28 µatm) is a result of higher variability in coastal grid cells compared to the open ocean; this is confirmed by a comparison to the offshore CCE1 mooring (Table B1), where the RMSE from the mooring-excluded RFR-CCS-Eval is just 10.5 µatm.

Figure 2 provides an example of one coastal mooring record (CCE2, which is positioned on the shelf break off the coast of Point Conception, CA, at 34.324∘ N, 120.814∘ W) compared to pCO2(sw) predicted in the corresponding grid cell (centered at 34.375∘ N, 120.875∘ W) by the mooring-excluded RFR-CCS-Eval model (Test 3) as well as the full RFR-CCS model. For comparison, pCO2(sw) in the same grid cell provided by the L17 coastal product is also shown. At the CCE2 mooring location, RFR-CCS reproduces mooring-observed monthly pCO2(sw) with a mean bias of -2.2 µatm and an RMSE of 16.1 µatm (R2=0.81). These error statistics are expected to be relatively favorable, as the RFR-CCS model is trained using mooring observations from CCE2. In contrast, the mooring-excluded RFR-CCS-Eval reproduces monthly mooring-observed pCO2(sw) at CCE2 with a mean bias of -4.6 µatm and an RMSE of 28.9 µatm (R2=0.41). This can be compared to the L17 coastal pCO2(sw) product, which reproduces monthly mooring-observed pCO2(sw) at CCE2 with a mean bias of -44.2 µatm and an RMSE of 57.3 µatm (R2=0.06). Notably, the mooring-excluded RFR-CCS-Eval captures pCO2(sw) variability at CCE2 more effectively than the L17 product, even though RFR-CCS-Eval was trained without mooring observations and the L17 training dataset (i.e., SOCATv4) includes CCE2 mooring observations through 2014. Similar results are obtained for comparisons to other mooring records (Table B1; Fig. B3), with RFR-CCS always producing the best error statistics (as expected) and RFR-CCS-Eval always producing a better R2 than L17, indicating that coastal seasonality at mooring locations is better captured by our regional random forest regression model, even when mooring observations themselves are not included in the model training. This is an important conclusion, especially in light of the recommendation by Hauck et al. (2020) that the inclusion of coastal areas and marginal seas in pCO2(sw) mapping methods will be critical for improving the ocean carbon sink estimate. If these areas are to be included, it is sensible to attempt to capture their unique modes of variability as accurately as possible.

Across the study area, values of pCO2(sw) from RFR-CCS were compared against corresponding values from L17 and L20. For temporal compatibility with L17 and L20, a climatology of average monthly values from RFR-CCS spanning 1998 to 2015 (RFR-CCS-clim) was created for these comparisons. Figure 3 shows mapped differences in annual means and seasonal amplitudes (calculated as the maximum climatological pCO2(sw) minus the minimum) of pCO2(sw) between RFR-CCS-clim versus L20 (top panels) and RFR-CCS-clim versus a climatological average of L17 (bottom panels); monthly mean differences in are given in Fig. B4.

The most notable feature of the annual mean difference maps is that RFR-CCS-clim produces much higher annual mean pCO2(sw) than both L17 and L20 in the nearshore coastal ocean and slightly higher pCO2(sw) in the remainder of the study area. Similarly, RFR-CCS-clim produces much higher seasonal variability than both L17 and L20 in the nearshore coastal ocean, especially north of about 34∘ N. On average, RFR-CCS-clim produces an area-weighted annual mean pCO2(sw) that is greater than L17 by 19.0 µatm and L20 by 8.4 µatm, as well as an area-weighted seasonal amplitude that is greater than L17 by 13.0 µatm and L20 by 5.6 µatm.

Values of pCO2(sw) from RFR-CCS, L17, and L20 were compared against the SOCATv4 gridded pCO2(sw) data product. SOCATv4 was used in the development of the coastal L17 product, whereas SOCATv5 was used in the development of the open-ocean product for the merged L20 climatology, and SOCATv2021 was used in the development of RFR-CCS. Therefore, comparisons were made to both the gridded open-ocean observations (1∘ resolution) and gridded coastal observations (0.25∘ resolution) from SOCATv4 to include only data points that were available to the training of all three data products. To match the resolution of the gridded open-ocean observations from SOCATv4, aggregation from a 0.25∘ resolution grid to a 1∘ resolution grid was performed for RFR-CCS, RFR-CCS-clim, and L20. L17 was only compared to gridded coastal observations from SOCATv4 because the two are gridded to the same spatial resolution and cover the same coastally limited spatial domain.

Figure 4 shows two-dimensional histograms of bin-averaged differences between RFR-CCS-clim, L20, RFR-CCS, and L17, each compared against gridded observations from SOCATv4. For comparisons to climatological products (RFR-CCS-clim and L20), gridded SOCATv4 observations were averaged to a monthly climatology across 1998–2015 for consistency with the products. The regional RFR-CCS product and its climatology outperform both global SOM-FFN products: RFR-CCS-clim shows better agreement with gridded monthly means of observations from SOCATv4 than L20 (R2=0.85 versus R2=0.73), and RFR-CCS (within the coastally limited spatial domain of L17) shows better agreement with gridded observations from SOCATv4 than L17 (R2=0.96 versus R2=0.61). In particular, the two global products (L20 and L17) struggle to match pCO2(sw) values in the nearshore coastal ocean (within 100 km of the coast), indicated by dark blue cells in Fig. 4.

Mismatches between global pCO2(sw) products and observations in the nearshore coastal ocean are not unexpected, as regional error statistics for reconstructed global pCO2(sw) are typically larger than the global mean error statistics (Laruelle et al., 2017; Landschützer et al., 2020c), and it is generally more challenging to model pCO2(sw) in environments with high temporal and spatial variability, such as in the nearshore coastal ocean (Landschützer et al., 2014). This result emphasizes the importance of carefully addressing nearshore pCO2(sw) when constructing global products if one hopes to achieve an accurate representation of coastal ocean variability. This may be achieved (1) by using a greater number of model clusters for coastal ocean reconstructions (L17 uses just 10 biogeochemical clusters for the global coastal ocean), (2) by increasing the spatial and/or temporal resolution of pCO2(sw) data products to better account for small-scale variability (Gregor et al., 2019), (3) by carefully accounting for mismatches between the temperature (and salinity) at which pCO2(sw) is measured versus that at which it is reported in surface data products (Ho and Schanze, 2020; Watson et al., 2020), or (4) by taking an ensemble approach to pCO2(sw) gap-filling to reduce errors overall, especially in undersampled regions (Gregor et al., 2019; Fay et al., 2021). Ultimately, it will be critical to continue to expand our observational capabilities by means of shipboard underway systems (Pierrot et al., 2009), uncrewed surface vehicles (Meinig et al., 2015; Sutton et al., 2021), biogeochemical Argo floats (Roemmich et al., 2019), moored buoys (Sutton et al., 2019), and other platforms, as well as to make strides toward incorporating these novel measurements into pCO2(sw) gap-filling schemes (Gregor et al., 2019; Djeutchouang et al., 2022).

Values of pCO2(sw) from RFR-CCS-clim, L17, and L20 were compared against monthly climatologies from mooring observations to evaluate how well each product captured seasonal variability at fixed time series sites. Figure 5 shows climatologies of mooring-observed pCO2(sw) (each averaged over available years and normalized to their annual mean) compared to pCO2(sw) from RFR-CCS-clim, L20, and climatological monthly averages of L17 (each normalized to their annual mean) in the grid cell corresponding to the mooring location. Overall, RFR-CCS-clim does a much better job of capturing the variability in mooring observations than either L17 or L20 (Table 4).

Three components comprised the estimate of uncertainty for pCO2(sw) values from RFR-CCS: observational uncertainty (θobs), mapping uncertainty (θmap), and gridding uncertainty (θgrid). According to the procedure detailed in Sect. 2.7, θobs was calculated as 3.3 µatm, θmap as 4.4 µatm for the open ocean and 35.3 µatm for the coastal ocean, and θgrid as 3.7 µatm for the open ocean (n=268) and 25.1 µatm for the coastal ocean (n=889). These three components were combined to obtain total pCO2(sw) uncertainty (θpCO2) according to Eq. (2), resulting in θpCO2 equal to 6.6 µatm for the open ocean and 43.4 µatm for the coastal ocean. The open-ocean value determined through this analysis compares well with the grid-level uncertainty estimated in open-ocean grid cells by Landschützer et al. (2014), which ranged from 8.6 to 17.7 µatm for different regions. The large coastal uncertainty value emphasizes the high degree of variability in monthly pCO2(sw) near ocean margins.

As noted in Sect. 2.7, uncertainties reported here are appropriate for a given grid cell (i.e., monthly 0.25∘ latitude by 0.25∘ longitude bin). Values averaged over time or over larger regions will have reduced pCO2(sw) (and CO2 flux) uncertainties due to the spatiotemporal correlation of pCO2(sw) and the autocorrelation features of the model error (e.g., Landschützer et al., 2014).

In the open ocean, relatively high pCO2(sw) values can be observed off southern Baja California (Fig. 6a) and extending toward the northwest, especially during summer months and into autumn (Fig. 7) when higher sea surface temperatures drive higher pCO2(sw) (Nakaoka et al., 2013). This area also corresponds to low chlorophyll (Fig. A2) and the lowest wind speeds across the study region (Fig. A4), suggesting that a lack of nutrient delivery from deep convection may be limiting biological production, also driving high pCO2(sw). Relatively low open-ocean pCO2(sw) values can be observed in the northern part of the study region from about 45 to 60∘ N (Fig. 6a). Wintertime cooling drives low pCO2(sw) in this area, though that effect is compensated for by dissolved inorganic carbon (DIC) brought to the surface by deep winter mixing (Ishii et al., 2014). Figure B5 illustrates competing effects between temperature and winds by displaying correlations between SST and pCO2(sw), which are mainly positive below 50∘ N, and between wind speed and pCO2(sw), which are mainly positive above 50∘ N.

In the summer, high biological production in the northern portion of the study region (Fig. A2) removes DIC, keeping pCO2(sw) relatively low. This low-pCO2(sw) region extends southward along the California coast to about 34∘ N between both offshore and nearshore high-pCO2(sw) waters. The southward extension of the low-pCO2(sw) region is consistent with what we know about the dynamics of the CCS: a narrow band of nearshore waters is high in DIC in the spring and summer due to the direct effects of wind-driven upwelling (Fig. 7), but a wider band of waters farther offshore is lower in DIC due to drawdown by high biological production stimulated by nutrients delivered to the euphotic zone by upwelling (Hales et al., 2005; Fassbender et al., 2011; Fiechter et al., 2014; Turi et al., 2014).

In the coastal ocean, high pCO2(sw) occurs in the central CCS (∼ 34 to ∼ 42∘ N), with values of 400 µatm or greater beginning in April off Pt. Conception (34∘ N) and propagating northward to around Cape Arago (43∘ N) through October (Fig. 7). This corresponds to the latitudinal band of the CCS with the strongest and most consistent equatorward winds (Huyer, 1983), which induce upwelling of CO2-rich subsurface waters by wind-driven Ekman transport very near the coast and wind-stress-curl-driven Ekman pumping farther offshore (Checkley and Barth, 2009). This nearshore band of high summertime pCO2(sw) has been previously reported by observational (Hales et al., 2012) and modeling (Fiechter et al., 2014; Turi et al., 2014; Deutsch et al., 2021) studies. It corresponds to naturally low surface pH values and aragonite saturation states, which will be exacerbated by increasing atmospheric CO2 concentrations (Gruber et al., 2012; Hauri et al., 2013), with likely deleterious effects for calcifying organisms (Feely et al., 2008).

Relatively low coastal pCO2(sw) values (340 µatm or lower) develop during April off the coasts of Oregon, Washington, and Vancouver Island and propagate northward toward southern Alaska through September (Fig. 7). Low summertime pCO2(sw) in the northern CCS (∼ 42 to ∼ 50∘ N) has been demonstrated before (Hales et al., 2005, 2012; Evans et al., 2011; Fassbender et al., 2018) and corresponds to the weaker and more variable equatorward winds in summer in the northern CCS (Checkley and Barth, 2009) as well as the effect of DIC drawdown by high primary productivity, which offsets upwelling-induced increases in pCO2(sw). Primary productivity in the northern CCS can be enhanced relative to the rest of the CCS due to factors like riverine nutrient delivery and distribution, submarine canyon-enhanced upwelling, and physical retention of phytoplankton blooms (Hickey and Banas, 2008).

The coastal ocean from Vancouver Island northward is a high-pCO2(sw) region from October to March (Fig. 7), which is broadly consistent with observations of high pCO2(sw) in the western Canadian coastal ocean during autumn and winter (Evans et al., 2012, 2022). This high pCO2(sw) is perhaps due to the influence of deep tidal mixing (Tortell et al., 2012) and wintertime light limitation of DIC drawdown by primary production. The northern coastal area shifts to a low-pCO2(sw) region from April to September, again consistent with observations (Evans et al., 2012, 2022) and likely reflecting surface DIC drawdown by primary production in the region (Ianson et al., 2003).

The coastal ocean from the Southern California Bight (SCB) southward along Baja California (∼ 22 to ∼ 34∘ N) shows relatively low pCO2(sw) seasonality (Fig. 6b). In this region, pCO2(sw) is generally lower than in offshore waters of the same latitude, which matches previous results well (Fig. 6a; Hales et al., 2012; Deutsch et al., 2021). One exception is directly off the southern tip of Baja California, where especially high summertime pCO2(sw) is observed. This may in part reflect the tendency for wind-driven upwelling to bring significant amounts of CO2-rich subsurface waters to the surface just south of major topographic features (Van Geen et al., 2000; Friederich et al., 2002; Fiechter et al., 2014). Coastal pCO2(sw) within the Gulf of California (GoC) appears to be strongly influenced by thermally induced seasonal effects, though the lack of observational data coverage in the GoC within SOCATv2021 (Fig. 1), especially within the nonsummer months (Fig. B1), may mask more dynamic variability.

The seasonal amplitude of pCO2(sw) (Fig. 6b) exhibits interesting variation in the central and northern CCS. Here, nearshore seasonality is extremely high due to dominant effects from upwelling and primary production; however, seasonality farther offshore is extremely low, likely due to compensating effects by thermally driven changes to pCO2(sw) (high temperature in summer increases pCO2(sw), low temperature in winter decreases pCO2(sw)) and biologically or physically driven changes to pCO2(sw) (high primary production in summer decreases pCO2(sw), deep mixing in winter increases pCO2(sw)). Elsewhere, a hotspot of high seasonality exists offshore around 40∘ N, possibly due to thermal control of pCO2(sw) without strong biophysical compensatory effects.

A recently published data product (SeaFlux; Gregor and Fay, 2021) described by Fay et al. (2021) harmonizes calculations of global CO2 flux by standardizing the areas covered by different global pCO2(sw) products and by scaling the gas exchange coefficient to different wind products. As part of this procedure, the L20 climatology is used to fill spatial gaps in some of the pCO2(sw) products. As we have demonstrated here, filling gaps with this climatology may result in an underestimate of the seasonal pCO2(sw) cycle in certain locations, especially nearshore (Fig. 5). For comparison we calculate monthly CO2 flux in our study region from SeaFlux and from RFR-CCS, resulting in the monthly climatologies shown in Fig. 8.

Overall, the SeaFlux ensemble (with ERA5 winds) suggests an oceanic uptake of 69.2 Tg C yr-1 for the RFR-CCS domain between 1998 and 2019 (inclusive) compared to an uptake of 60.0 Tg C yr-1 calculated from RFR-CCS. Of the excess 9.2 Tg C yr-1 uptake from SeaFlux, 5.7 Tg C yr-1 comes from the open ocean and 3.5 Tg C yr-1 from the nearshore coastal ocean (within 100 km of the coast). Given that the nearshore coastal ocean only comprises about 9 % of the RFR-CCS region yet ∼ 38 % of the discrepancy, the discrepancy in coastal uptake is more significant on a per area basis than the open-ocean discrepancy, as can be observed visually in Fig. 8. This discrepancy may reflect more coastal outgassing captured by RFR-CCS than the SeaFlux ensemble, consistent with the annual mean differences shown in Fig. 3a and c. Still, the RFR-CCS results do lie within the variability of SeaFlux pCO2(sw) products (Fig. 8a and b).

RFR-CCS includes pCO2(sw) values for the coastal and offshore ocean in the northeastern Pacific that are representative of monthly conditions. However, air–sea carbon dioxide exchange, which is driven by the difference between oceanic and atmospheric pCO2, operates on shorter timescales. It has been demonstrated in the past that inadequate sampling frequency can be a significant factor biasing CO2 flux (FCO2) estimates (e.g., Monteiro et al., 2015).

To demonstrate this potential bias, Fig. 9 shows FCO2 at the CCE2 mooring over the course of 2015 (1) calculated from RFR-CCS monthly pCO2(sw) matched to NOAA marine boundary layer monthly pCO2(atm) and monthly averages of squared 3-hourly ERA5 winds (blue), (2) calculated from 3-hourly mooring measurements of pCO2(sw) and pCO2(atm) matched to squared 3-hourly ERA5 winds (grey), and (3) as the 1-standard-deviation envelope obtained by the following Monte Carlo process: assigning one randomly selected pair of 3-hourly mooring measurements of pCO2(sw) and pCO2(atm) from each month as the monthly values, matching them with squared 3-hourly ERA5 winds to calculate FCO2, and repeating this 100 000 times to obtain statistically meaningful values (green).

The FCO2 values provided by the 3-hourly mooring measurements are as close as possible to the true flux. Those provided by RFR-CCS are a best-case scenario for monthly flux approximations in the absence of continuous measurements (because the RFR model was trained on monthly mean pCO2(sw) values from 3-hourly observations at CCE2). Those provided by the Monte Carlo analysis provided reasonable ranges of FCO2 that might be obtained from sporadic sampling of one measurement per month without the benefit of an advanced interpolation routine like RFR-CCS. The annual FCO2 calculated from RFR-CCS (-0.26 mol C m-2 yr-1) agrees fairly well with that from the 3-hourly mooring measurements (-0.18 mol C m-2 yr-1). The smaller uptake from the mooring measurements likely reflects the effect of transient outgassing events in the spring and summer, when positive ΔpCO2 coincides with high wind speeds. The range from the Monte Carlo analysis (-0.00 to -0.36 mol C m-2 yr-1) highlights the variety of outcomes in calculated FCO2 that might result from sporadic sampling in the coastal ocean, representative of a region with no high-resolution mooring measurements that may be observed by a ship's underway system only a few times a year.

In large portions of the open ocean, low temporal variability and high spatial correlation mean that the aliasing problem may be a relatively low-priority concern for calculations of FCO2 from sporadic pCO2(sw) measurements (Bushinsky et al., 2019). However, the dynamic coastal ocean is dominated by processes that influence pCO2(sw) and FCO2 on short spatial and temporal scales, making observational frequency a significant factor that can bias annual FCO2 calculations. This bolsters the case for the expansion and enhancement of coastal carbon observing systems even with pCO2(sw) gap-filling methods, such as the one described here, at our disposal.