BGC-Argo floats are equipped with five to six sensors including 1) a CTD (conductivity, temperature, and depth), chemical sensors capable of measuring 2) dissolved oxygen, 3) nitrate, 4) pH on the total scale (henceforth pH, measured at in situ temperature and pressure) (Marion et al., 2011; Waters and Millero, 2013), 5) a bio-optical sensor capable of measuring chlorophyll fluorescence, and particulate backscatter (Riser et al., 2018; Bittig et al., 2019; Chai et al., 2020) and 6) a downwelling irradiance sensor capable of measuring light penetration (Organelli et al., 2017). Four GOM BGC-Argo floats were deployed in September-October 2021 and in June of 2023 (see float model and sensor details in Table 1 ). Generally, on 10-day intervals, the GOM floats collected a vertical profile from 2,000 m during its ascent to the sea surface. Between profiles, the GOM floats have been programmed to park at 1,500 m (rather than 1,000 m standard park depth) where they passively drift between cycles. A total of 205 float profiles have been collected by the GOM array during the first two years of operation ( Figure 1 ). Sensor failures for two floats ( Table 1 ), diagnosed using the transmitted sensor engineering files, resulted in abrupt and dramaticaly drifting pH profiles with clearly unreasonable values (e.g. values of <5). Excluding these profiles, a subset of 103 pH profiles (inclusive of pH profiles effected by pH pump offset) out of the 205 total collected BGC-float profiles have pH data that are included in this analysis.

Following the delayed mode quality control (DMQC) methodology of Wong et al. (2024), for float CTD and trajectory data, we confirmed that no adjustments for our float CTD data were required. This is unsurprising as typically only 15% of the “core Argo’’ parameters (i.e. temperature and salinity) require adjustment. Conversely, DMQC adjustments are always required for float oxygen, nitrate, and pH sensor data. We determined and applied corrections for float oxygen, nitrate, and pH profiles using the methodology and Sage-O2 and Sage software developed by Maurer et al. (2021). For pH and nitrate corrections, we applied a reference depth of 1480-1520 m and ESPER-NN to estimate local deep reference values. A series of up to 16 ESPER neural network equations were applied within the Sage software and the output with the lowest associated uncertainty is returned and used to calculate and then apply a reference depth offset. Equation 7 used in our study (see Table 2 for inputs), is also used by Sage to in part determine float pH corrections. Following DMQC corrections, reported float sensor accuracy for in-air corrected or World Ocean Atlas climatology corrected oxygen are 1% (Maurer et al., 2021) and 3% (Takeshita et al., 2013) of surface oxygen values, respectively. Oxygen sensor data uncertainty propagate, adding an additional source of uncertainty, when float oxygen data are used as input parameters to derive a deep reference value for nitrate and pH DMQC or algorithm estimated values. Reported BGC float nitrate and pH sensor accuracies are within 0.5 μmol kg-1 190 and 0.007 pH units, respectively (Johnson et al., 2017; Maurer et al., 2021).

Several GOM floats demonstrated pH offset, resulting in profile shifts at 1,000 m between >0.01 pH units. The offset manifests at 1,000 m due to the pH sensor being plumbed into the CTD pump line and at this depth the CTD enters into a continuous pumping mode as it increases sampling resolution for the upper half of the profile. The proposed DMQC protocol for adjusting pump offset float profiles (visible offset in pH > 0.01) is to use a shallower reference depth to a value that is above the pump on depth (typically 1,000 m), and to flag the deeper portion of the profile as bad (Johnson et al., 2023). While a correction approach has been proposed for dealing with pump offset profiles, the root cause of the sensor behavior has not been fully characterized (Johnson et al., 2023). Due to magnitude of the offsets observed and the lack of confidence we felt in deriving and applying this correction factor, we chose to not apply a pump offset correction. Rather, these data were included to demonstrate the utility of using neural network approaches to diagnose sensor behavior.

The GOM-NN_pH algorithm was developed using MATLAB’s deep learning toolbox. The architecture was designed to optimally estimate pH by using inputs of BGC-Argo float data. A neural network, which is a supervised machine learning model, was selected to be trained and applied with GOMECC data as it achieved superior performance over random forest and multiple linear regression models during algorithm development testing. The GOM-NN_pH is a feed-forward neural network that contains two hidden layers ( Figure 2 ). A total of four GOM-NN_pH algorithms were trained with various combinations of predictors. The number of neurons in each hidden layer corresponds to the number of input parameters utilized in a given algorithm. The predictor variables within the input layer were given varying weights for each neuron in the algorithm design. When training the two-layer networks, data were randomly divided into three subsets: 70% for training, 15% for validation, and 15% for testing that were used during the neural network training process. The Levenberg-Marquardt optimization algorithm (Hagan and Menhaj, 1994), was used in the training process with a performance metric of mean squared error. Each algorithm was trained using 1,000 iterations using the algorithm specific GOMECC dataset.

The GOMECC bottle dataset represents the largest source of GOM carbonate chemistry data (Wanninkhof et al., 2013; Wanninkhof and Baringer, 2014; Barbero et al., 2019, 2024), that have equal data quality to the GO-SHIP Program (Sloyan et al., 2019). GOMECC has routinely reoccupied a series of cross shelf transects that terminate in the deep GOM basin, with a growing number of transect locations having been added to the GOMECC program in the GOM since its inception. A subset of the GOMECC data were mined for training and validation of the GOM-NN_pH algorithms based on several criteria ( Figure 1 ). First, only GOMECC cruises that included spectrophotometric pH measurements at 25˚C were utilized. This resulted in the exclusion of GOMECC-1 data (2007) where carbonate system variables were measured (Dissolved Inorganic Carbon (DIC), Total Alkalinity (TA), and CO₂ fugacity (fCO₂) but did not include direct measurements of pH. Second, we incorporated only open GOM stations (minimum of 1,000 m water column) to coincide with the open GOM water masses where BGC-Argo floats are operating. The exclusion of shallower stations eliminates complex carbonate system dynamics that exist along GOM continental margins, particularly the effects of large riverine outflows (e.g., Huang et al., 2015; Osborne et al., 2022), which would likely not be well parameterized by the GOMECC dataset.

We chose to hold back the GOMECC Tampa Line stations (n = 4 profiles), which are located off of the West Florida Shelf ( Figure 1 , orange symbols). These stations were reoccupied during GOMECC-2 (July-2012), GOMECC-3 (July-2017), and GOMECC-4 (September-2021) and were used as an external, independent validation dataset. Our motive in holding back the Tampa Line bottle data was to test the performance of the GOM-NN_pH with a region of the GOM where no training data was used in the algorithm development.

GOMECC data utilized in the GOM-NN_pH algorithms include CTD measured temperature, salinity, and pressure, Winkler titration oxygen, colorimetric measurements of nitrate made onboard using an autoanalyzer, and spectrophotometric pH (measured onboard at 25˚C). Following best practices (Hood et al., 2010), calibrants and reference material determined accuracies based on replicates indicated O₂ <2 µmol kg^-1; Nitrate < 0.1 µmol kg^-1; and pH < 0.002. GOMECC calibrated CTD temperature and salinity profile uncertainties are within WOCE standards, 0.002°C and 0.002 PSU, respectively. Shoreside secondary quality control was executed and WOCE quality control flags were applied and only data flagged as ‘good’ or ‘replicate’ were used.

A direct comparison between bottle and float data requires a conversion of bottle spectrophotometric pH, measured onboard at 25°C and ambient atmospheric pressure, to in situ temperature and pressure pH. This conversion was completed using CO2Sys MATLAB with inputs of in situ temperature, salinity, pressure, phosphate, silicate, dissolved inorganic carbon, and pH (Van Heuven et al., 2009). Following the recommendations from Dickson et al. (2007), the constants for carbonic acid K1 and K2 from Lueker et al. (2000), the borate-to-salinity relationship from Lee et al. (2010), the constant for hydrogen fluoride KF from Perez and Fraga (1987), and the constant for hydrogen sulfate KS from Dickson (1990) were used. For the purpose of our study, bottle pH data that has been converted to in situ temperature and pressure are exclusively utilized in our study to permit a direct comparison with sensor pH results.

The quality of predictions generated by each of the GOM-NN_pH algorithms are reported in terms of goodness of fit (R²) and Root Mean Square Error (RMSE) between the measured and neural network predicted values ( Table 2 ; Figure 3 ). The RMSE is especially useful, as it is in the same units as the original data and therefore can be compared directly to measurement uncertainties. Generally, algorithms with more input predictors tend to perform better when the predictor measurements are high quality (Carter et al., 2021). While Equation 3 and Equation 4 show skill when compared to the training data ( Table 2 ; Figure 3 ), their performance is relatively weaker than Equations 1 and 2. This result highlights the importance of biogeochemical variables as a predictor of pH. Equation 4, trained using only physical predictors, demonstrates a negative bias in the upper pH range (>8) in the independent Tampa Line validation test. Equations 1 and 2 perform comparably and yielded with the same R² value (0.99). Equation 1 yields a lower RMSE (0.006 pH units) relative to Equation 2 (0.009 pH units) based on the training dataset ( Table 2 ). Validation results based on the application of Equations 1 and 2 to the GOMECC Tampa Line validation data yields marginally better results for Equation 2 relative to Equation 1 (RMSE 0.001 pH unit difference, Table 2 ). A paired t-test preformed on the neural network pH variances from the bottle validation (for the available overlapping data n = 144) indicate that the difference between the two model results is significant (p<0.001). Performance of Equation 2 based on the RMSE (Equation 2 = 0.007 pH units versus Equation 1 = 0.010 pH units) and mean absolute error (MAE) (Equation 2 = 0.005 pH units versus Equation 1 = 0.006 pH units) but suggests that Equation 2 performs marginally better when applied to the independent Tampa Line validation dataset. The training of Equation 2 benefited from a larger training and validation dataset, due to greater availability of oxygen relative to nitrate data in the GOMECC data selection. Equation 1 includes validation only from 2017 and 2021 due to no usable nitrate data available along the Tampa line in 2012. For these reasons, combined with the lowest BGC-Argo sensor uncertainties being associated with CTD and oxygen optode data, we chose to apply Equation 2 for to our GOM BGC-Argo dataset for the remained of the detailed assessment performed in our study.

We assessed the performance of the GOM-NN_pH relative to two globally trained algorithms that include a vastly larger training and validation dataset (10,000’s to 100,000’s data points) (Bittig et al., 2018; Carter et al., 2021). We compare our GOM-NN_pH Equation 2 to ESPER Equation 7 and CANYON-B (which has parallel input predictors) using the GOMECC Tampa Line data ( Figure 1 ) that was held back from the GOM-NN_pH training process. Our statistical results suggest a similar robustness in performance across the algorithms, with a slightly better RMSE reported for the GOM-NN_pH algorithm (0.009 pH units) relative to ESPER (0.010 pH units) and CANYON-B (0.012 pH units) ( Figure 4 ). The MAE for the GOM-NN_pH is also marginally lower (0.007 pH units) relative to ESPER (0.008 pH units) and CANYON-B (0.009 pH units) ( Figure 4 ).

Visualizing the algorithm variations from the observed validation data for the two algorithms in depth space, shows that there are notable differences among the GOM-NN_pH, ESPER, and CANYON-B outputs ( Figure 5 ). While the RSME is similar, the pattered biases in ESPER- and CANYON-B-generated estimates are considerable compared GOM-NN_pH. In the deep portion of the water column >1500 m, ESPER and CANYON-B both produce a notable positive bias, that result in pH values that are as much as 0.01 and 0.03 pH units higher than the GOM observations ( Figure 5 ). ESPER and CANYON-B demonstrate spurious behavior within the pH minima (typically ~600 m within the GOM) that also results in a distinctive positive bias. Differences between GOM-NN_pH algorithm outputs and observations are greatest at the surface, ranging from -0.025 to 0.01 (excluding outliers), which is on par with the variations observed for ESPER and CAYON-B at the surface ( Figure 5 ).

Shipboard bottle data provides an independent, high quality validation data source that can be used to quantify the differences between sensor and neural network algorithm pH estimates. A direct comparison of these datasets is possible for the first float profile when a CTD cast is collected at the time of deployment. For the neural network assessment, outputs generated by GOM-NN_pH Equation 2, ESPER Equation 7, CANYON-B, which each utilize latitude, longitude, pressure, temperature, salinity, and oxygen, were employed. Comparisons using depth-equivalent float and discrete bottle data, referred to as “matchups”, are reported following the approach described by Johnson et al. (2017).

There are important sensor-bottle matchup caveats to recognize. Float sensors can undergo significant drift due to sensor conditioning during the ~1-5 profile collections, with the greatest offsets often associated with the first collected profile. Johnson et al. (2017) attempted to overcome this limitation by matching bottle data collected at the time of deployment with the second profile collected by the float ~10 days later. Further, it is possible that depth-derived matchups that have temporal offsets that may be influenced by internal waves that would produce offsets between the bottle validation data that are the result of natural variability. It is possible to overcome the influence of internal waves by producing matchups based on density rather than depth, however we have chosen to report depth-based matchups in order to compare directly to previously published results (Johnson et al., 2017; Maurer et al., 2021). With these caveats in mind, the matchup comparison is the only means of comparing equivalent sensor, neural network, with bottle validation data.

CTD validation casts collected at the approximate site and time of float deployment for BGC-Argo floats 4903624, 4903625, and 7901009 are compared to the first and second profiles collected by each float ( Figure 6 ; Table 3 ). Note that BGC-Argo float 7901009 (Navis float) only reached 1,150 m during its first profile, as Navis BGC-Argo floats undergo an auto-ballasting process that enables the float to reach its full profiling depth of 2,000 m over the first few cycles of operation ( Figure 6 ). Less than 24 hours elapses between the start time of the matchup CTD and the transmission time of the first float profile at the end of the profile collection, which takes on average ~6 hours to collect. The second float profile was collected approximately 10 days following the first profile. Figure 6 demonstrates the significant differences between the first and second float sensor pH profiles collected 10 days apart by float 4903625 that are a result of natural variability. Based on a satellite-based assessment (see method described in McWhorter et al., 2024), the first profile and validation cast for float 4903625 are collected in GOM Common Water and over the next 10 days, this float drifted into the Loop Current where profile two was collected. This demonstrates that major biogeochemical variability can exists over small spatial scales in the GOM, necessitating that matchups compare contemporaneous data collections when possible.

The matchup results show that the neural network pH results match the validation more closely than sensor pH. The largest matchup differences are associated with the float sensor data in the upper 1000 meters of the water column, which appear to increase with decreasing pressure ( Figure 6 ). Across the full depth range for all GOM float sensor matchups, a median offset of -0.022 pH units is observed ( Table 3 ). This is significantly higher than the 0.002 median offset determined in a bottle matchup analysis of globally distributed BGC-Argo floats (Maurer et al., 2021). Recall the caveat that sensor conditioning that can occur during the first several float profile collections may be exacerbating these bottle-sensor offsets. The convergence of all datasets at depth with the validation data suggest that sensor conditioning is not the only potential influence on surface value offsets observed in the sensor dataset. An additional comparison of the sensor pH differences from the three neural network pH estimates for the bottle validation dataset further illustrates a positively correlated pressure-dependent offset in the sensor pH dataset ( Figure 7 ).

Two of the GOM Apex floats, 4903622 and 4903625, demonstrated pH-pump offset, evidenced by abrupt shifts in pH values between the ~950 and ~1000 dbar ( Figure 8 ). Based on a visual assessment and comparison with bottle matchup and GOM-NN_pH estimates, we approximate that the pH pump offset causes offsets in the first float profiles of -0.014 pH units for 4903624 and 0.021 pH units for 4903625. Application of these corrections across the upper half of the profile vastly improves the matchup RMSE for float 4903625 (RMSE 0.009 pH units), however it only moderately improves the RMSE for 4903624 (RMSE 0.020 pH units). For both floats, but especially for 4903624, corrected profiles continue to show considerable offsets from the validation data and neural network results ( Figure 8 ). And float 7901009, which is unaffected by pH pump-offset, also appears to show inversely related pressure-dependent differences ( Figure 6 ).

The visual inspection approach using profile 1 relies on the availability of the bottle data, which are limited by the potential for sensor conditioning-related variations. Therefore, exclusive use of bottle validation data to identify a float pump-offset correction factors is an imperfect approach. Further, applying a blanket correction across the full collection of float profiles is unreliable, as the pump-offset may not be stable over time. Ideally, profile specific pH-pump offsets are determined, which can be generated, for example, using neural network simulations of pH. Sensor and neural network profiles can be directly compared in an attempt to diagnose sensor behavior and potentially quantify an appropriate offset. However, quantifying the propagation of uncertainty and a general assessment of various correction approaches is still needed. The current standard for correcting pH pump-offset, which suggests the shoaling of the reference depth to <1000 m (above the pump on depth) (Johnson et al., 2023), can introduce other uncertainties during the DMQC process. Specifically in the GOM, biogeochemical variability related to the Loop Current can be induced at 1000 m, therefore this cannot be assumed to be a stable reference depth. For this reason, we choose to not publish a pH pump-corrected dataset associated with our floats as to not publish data we are not confident in.

The non-pH pump-offset corrected BGC-Argo sensor data-bottle validation matchups, collected in association with the first float profile, are summarized in Table 3 . A total n = 43 bottle matchups are available across our dataset. GOM-NN_pH pH estimates were generated to directly compare NN-bottle to the float-bottle matchup results. Based on the mean, there are highly significant differences (t-test p <0.005) between the algorithm matchup compared to the BGC-Argo float pH sensor matchup. Matchup offsets are consistently greater in the BGC-Argo pH sensor dataset, which are visualized in Figure 9 , demonstrating the considerable float negative pH bias in the upper 1,000 m of the water column observed for all three floats, which becomes larger with decreasing pressure.

Based on the bottle matchup assessment for the full GOM BGG float array, we report a MAE of 0.025 and RMSE of 0.030 pH units ( Table 3 ). Previously, the pH sensor uncertainty across the large BGC-Argo arrays has been reported as half of one standard deviation based on bottle-float matchups (Maurer et al., 2021). This hinges on the assumption that half of the variability between a bottle validation cast and the first float profile is the result of natural ocean variability (Johnson et al., 2017). Based on the error approach reported in Maurer et al. (2021), the GOM array yields a 0.009 pH unit uncertainty, which is on par with the reported uncertainty of 0.007 from a meta-analysis of globally distributed BGC-Argo floats (Johnson et al., 2017; Maurer et al., 2021). Overall, the GOM-NN_pH algorithm yields the most robust matchups, with an RMSE of 0.008 pH units and an adjusted uncertainty (half of one standard deviation) of 0.004 ( Table 3 ).

We further assess performance of the GOM BGC-Argo pH sensors by calculating mean pH profiles for all sensor pH profiles and GOM-NN_pH profile estimates per float ( Figure 10 ). Mean pH profiles represent averaged values across a series of binned depths for all cycles collected over the lifetime of a given float. This assessment ingests a much larger dataset (n profiles = 103, n data points = 11870 per data type) relative to the currently available matchup validation dataset (n profiles = 3, n data points = 43 per data type) and overcomes the caveat that validation matchups with the first float profiles can be hindered by sensor conditioning that can yield magnified sensor biases during the first few float cycles of float operation.

Consistent with the validation matchups, the mean profile comparisons between sensor pH and GOM-NN_pH estimated pH demonstrate the highest differences between datasets over the upper 1,000 m. For floats 4903624 and 4903625 this is in part due to an uncorrected pH pump-offset. While application of a tentative pH pump-offset correction for float 4903625 improves the sensor-GOM-NN_pH alignment, a considerable pressure dependent difference remains for float 4903624 and is also present for float 7901009. Figure 10 illustrates the particularly prominent pH pump-offset for float 4903625 and observable but smaller for float 4903624. The results of the mean profile comparison qualitatively confirm the observations made based on the significantly smaller validation dataset used in the matchup assessment.