**2. Materials and Methods**

#### *2.1. Study Area*

The study area covers part of the Atlantic Ocean, comprising part of the Iberian Plain, with the Canary basin on the east side and the North American basin on the western side, reaching to the Puerto Rico trench.

Time series measurements show that the North and Central Atlantic constitutes the largest reservoir of anthropogenic CO2 [15–17] and displays a surface ocean pH decline [18]. Moreover, a strong correlation between the *p*CO2 and the surface water pH was identified by Bates et al., 2012 [19], with the latter showing a definitive decrease in the North Atlantic Ocean between 1984 and 2012. Furthermore, in its 2015 and 2016 State of the Climate, NOAA reported a world record in terms of large sea surface temperature and upper ocean heat content anomalies in large swaths of the western North Atlantic Ocean [20,21]. This extreme event can offer an interesting opportunity to continue studying the changes in DIC, with respect to pH, TA, and sea temperature [22], whilst making use of the novelty of this study.

#### *2.2. Field Data*

This study made use of the best surface underway data available over the study area for the period of 2015–2016. The Ocean Carbon and Acidification Data Portal of the National Centers for Environmental Information provides only one set of surface underway data (NCEI Accession 0154382) that contains the three core study variables of DIC, TA, and pH over the study area covering the period of analysis (https://www.ncei.noaa.gov/data/oceans/ ncei/ocads/metadata/0154382.html (accessed on 20 February 2023)). Additional surface underway datasets are available; however, these consist of an increasingly limited number of observations (such as NCEI Accession 0157237, 0157352, 0157312, and 0110259), for which suitable co-located and co-temporal satellite and model reanalysis data are not available.

#### 2.2.1. In Situ Observations of the Carbonate System

From 7 March 2015 to 6 November 2016, the M/V Equinox (ID: MLCE) sailed across the North Atlantic Ocean three times. Discrete surface underway measurements of seawater DIC, TA, and pH were performed on all cruises (Figure 1). The details of the laboratory methods onboard the M/V Equinox are well documented [23] as NCEI Accession 0154382. This research was conducted in support of the coastal monitoring and research objectives of the NOAA Ocean Acidification Program (OAP) and the Climate Program Office. The research cruise covered an area from −78.9797◦ W to −10.3998◦ E and from 38.4622◦ N to 19.2893◦ S.

In addition to DIC, TA, and pH, M/V Equinox also collected sea surface temperature and sea surface salinity measurements with a documented uncertainty of ±0.001 ◦C and ±0.005%, respectively (see https://www.ncei.noaa.gov/data/oceans/ncei/ocads/ metadata/0154382.html (accessed on 20 February 2023)). The range of the values collected during the cruise mission is shown in Table 1.

**Figure 1.** Sampling periods of in situ discrete underway samples of DIC, TA, and pH measured by M/V Equinox (source: NCEI Accession 0154382) overlaid over bathymetry (source: GEBCO) for Longitude −80◦ to −10◦ and Latitude +18◦ to +40◦. Inset: Winter 2015: Validation dataset 1; Autumn 2016: Validation dataset 2; Spring 2015: Validation dataset 3; Spring 2016: ANN training dataset. The observations along the red transect were used to train the ANN for the prediction of DIC, TA, and pH. The surface underway measurements shown in brown, yellow, and green were used to validate the ANN algorithm against other independent datasets.


**Table 1.** Data value range and difference Δ along the transects M/V Equinox (ID: MLCE NCEI Accession 0154382) for the entire cruise period.
