**Hindcast Biochemistry Data**

In order to extend the validation of our BPN algorithm, additional independent sources of daily and/or monthly 2016 oceanic surface pH maps were sought; however, this type of dataset proved to be scarce, whilst 2016 daily/monthly gridded oceanic TA and DIC data are non-existent. As of now, the Copernicus Marine Service (CMEMS) makes available the following three datasets: (1) the Global Ocean Biochemistry Hindcast, which consists of both daily and monthly gridded maps (however, the geographic information about pH is only available at a monthly temporal resolution at 0.25◦ by 0.25◦ grid resolution); (2) the Global Ocean—in situ reprocessed carbon observations—SOCATv2021, which provides point measurements of DIC, TA, and pH, such as NCEI Accession 0154382; and (3) the Global Ocean Surface Carbon database, which provides pH data on a monthly basis at 1◦ by 1◦ grid resolution.

The correlation between the modeled pH (for 30 November 2016) and that derived from the Global Ocean Biochemistry Hindcast (16 October–15 November 2016 at 00:00 h UT) over the area of study is shown in Figure 9. This hindcast database provides monthly data starting as of the 16th day of each month, and therefore this data represents the average value for an entire month. In spite of their slight temporal difference, the two datasets are shown to be strongly correlated together, with an R2 of 0.81 (Figure 9c), indicating a good statistical similarity, as well as an impressive spatial similarity for pH (Figure 9a,b). From an atmosphere–ocean dynamical point of view, this correlation points to a slowly changing pH distribution for the study area over a monthly scale.

**Figure 9.** *Cont*.

**Figure 9.** pH distribution map (**a**) ANN-estimated pH valid for 30 October 2016; (**b**) extracted from the Global Ocean Biochemistry Hindcast valid for 16 October–15 November 2016, and (**c**) scatterplot between (**a**) and (**b**) (R<sup>2</sup> = 0.81).
