Pressure and salinity sensitivity for the RBRcoda OpH sensor

Pressure sensitivity

RBR measured the pressure response directly on the PK8T sensor spot across its full 0 to 6000dbar rating and applies a correction of 0.023 ± 0.002pH per 1000dbar. Wirth et al. (2024) assessed the same optical pH sensor and reported a comparable value of 0.029pH per 1000dbar, which was only validated to 2000dbar. RBR extended the measurement to the full 6000dbar rating, and the pressure response showed no measurable hysteresis.

Salinity sensitivity

If logged salinity data is not available, an approximate value is sufficient in seawater: near 35PSU, a salinity input within 10PSU of the true value changes the reading by less than 8mpH. The effect is larger in low-salinity water: near 5PSU, an input off by only 2PSU changes the reading by roughly 19mpH.

Equations

Corrected pH equation as used in the RBRcoda OpH is a condensed version of the full salinity compensation shown in equations (2) and (3).

\[pH_{corrected} = pH - \frac{1}{2}\,g0\left(\frac{\sqrt{IS}}{1+\sqrt{IS}} - 0.2791745 - g1\,(IS - 0.15)\right) - k\,P, \quad IS = \frac{20\,S}{1000} = \frac{S}{50} \ (1)\]

where pH is the uncompensated reading, S is salinity (g/L), P is pressure (dbar), g0 = 0.970 and g1 = 0.126 are the ionic-strength (activity) coefficients, and k = 2.337 × 10⁻⁵pH/dbar is the pressure sensitivity. The salinity term is zero at the reference ionic strength IS = 0.15 (S = 7.5g/L).

Full expanded form (substituting the uncompensated conversion, with raw ratio R and temperature-corrected coefficients c1′, c3′, c5′, c7′):

\[pH_{corrected} = c5^{\prime}\,\log_{10}\!\left(\frac{c1^{\prime} - R}{R - c3^{\prime}}\right) + c7^{\prime} + c8 - \frac{1}{2}\,g0\left(\frac{\sqrt{IS}}{1+\sqrt{IS}} - 0.2791745 - g1\,(IS - 0.15)\right) - k\,P \ (2)\]

Salinity sensitivity of pH, full correction equation. This is the derivative ∂pH/∂S of the salinity term in equation (1), independent of the pH reading and temperature:

\[\frac{\partial pH}{\partial S} = -\frac{g0}{100}\left(\frac{1}{2\sqrt{IS}\,(1+\sqrt{IS})^{2}} - g1\right) \quad [\text{per g/L}] \ (3)\]

Verified against equation (1) with g0 = 0.970, g1 = 0.126. In seawater (~35g/L) the sensitivity is about −0.5 mpH per PSU; it grows sharply below ~15PSU (about −4mpH per g/L at 10g/L), which is why low-salinity deployments need an accurate salinity value.

Salinity (g/L)	Correction (mpH)	∂pH/∂S (mpH per g/L)
5	+16	−7.6
10	−11	−4.0
20	−37	−1.7
35	−52	−0.5
45	−55	−0.1

Salinity (g/L)

Correction (mpH)

∂pH/∂S (mpH per g/L)

+16

−7.6

−11

−4.0

−37

−1.7

−52

−0.5

−55

−0.1

Reference

Wirth, T., Takeshita, Y., Davis, B., Park, E., Hu, I., Huffard, C. L., Johnson, K. S., Nicholson, D., Staudinger, C., Warren, J. K., & Martz, T. (2024). Assessment of a pH optode for oceanographic moored and profiling applications. Limnology and Oceanography: Methods, 22(11), 805–822. https://doi.org/10.1002/lom3.10646