*2.5. Error Analysis*

The uncertainty in pH arose from the pH measurement process. The uncertainty in TA is from the measured salinity and the TA–S Equation (1). The uncertainty in (TA2)mix and (DIC2)mix is introduced during the determination of the three endmembers. The uncertainty in DIC, *p*CO2water, *p*CO2bio, potential *p*CO2, and *p*CO2bio originates from CO2SYS with the equilibrium constants established by Mehrbach et al. [41] and refit by Dickson and Millero [39] (i.e., with carbonic acid dissociation constants omitted from calculations). The uncertainty in FCO2, FCO2bio, \*FCO2, and \*FCO2bio arises from the calculation using the daily gas transfer velocity (k) and deviations in *p*CO2water and *p*CO2bio. In this study, we used error propagation formulas to estimate the uncertainties [42].

Assuming that the errors of the variables X, Y, and Z are δX, δY, and δZ, respectively, for linear sum functions, the error of R is

$$R = \mathbb{X} + \mathbb{Y} + \mathbb{Z} \tag{27}$$

$$
\delta \mathcal{R} = \delta \mathcal{X} + \delta \mathcal{Y} + \delta Z \tag{28}
$$

For multiplication and division, the error of R is

$$\mathbf{R} = (\mathbf{\hat{x}} \times \mathbf{\hat{y}}) \mathbf{Z} \tag{29}$$

$$(\delta \mathbf{R} \mathbf{/R})^2 = (\delta \mathbf{X} \langle \mathbf{X} \rangle^2 + (\delta \mathbf{Y} \langle \mathbf{Y} \rangle)^2 + (\delta \mathbf{Z} \langle \mathbf{Z} \rangle^2)^2 \tag{30}$$

Overall, the uncertainty in the salinity-based TA calculation is less than 3%; the uncertainties in (TA2)mix and (DIC2)mix are ~0.4% and ~0.8%, respectively; the uncertainty in k is ~13%; the uncertainty of FCO2, FCO2bio, \*FCO2, and \*FCO2bio is ±1.61, ±2.10, ±2.61, and ±0.86 mmol m<sup>−</sup><sup>2</sup> day−1, respectively.
