O2 saturation derived from concentration

Consider an RBRconcerto³ with an integrated RBRcoda³ T.ODO or Aanderaa Optode DO sensor . The dissolved oxygen sensor transfers both the foil temperature and the dissolved oxygen concentration (not compensated for salinity). The RBRconcerto³ calculates the concentration compensated for salinity first, then the air saturation (in %) via the following equation:

$//<![CDATA[ \begin{array}{l}\text{Air saturation} = 2.24457 \cdot \dfrac{(10.1325 - Pav) \cdot Cc}{(Patm - Pav) \cdot \text{Solubility}}\end{array} //]]>$

where

• Cc is the concentration in uMol/L, compensated for salinity,
• Patm is atmospheric pressure, and
• Pav is air vapour pressure.

Solubility is calculated via Gordon and Garcia as:

$//<![CDATA[ \begin{array}{l}\begin{equation*} \begin{aligned} \text{Solubility} = exp((&Ga_0 + Ga_1 \cdot Ts + Ga_2 \cdot Ts^2 + Ga_3 \cdot Ts^3 + Ga_4 \cdot Ts^4 + Ga_5 \cdot Ts^5) \\ + S \cdot (&Gb_0 + Gb_1 \cdot Ts + Gb_2 \cdot Ts^2 + Gb_3 \cdot Ts^3) + Gc_0 \cdot S^2) \end{aligned} \end{equation*}\end{array} //]]>$

where S is the salinity in PSU and Ts is defined as:

$//<![CDATA[ \begin{array}{l}Ts = ln(\dfrac{298.15 - T}{273.15 + T})\end{array} //]]>$

with T being the water temperature in °C and:

$//<![CDATA[ \begin{array}{l}\begin{equation*} \begin{aligned} Ga_0 & = 2.00856 \\ Ga_1 & = 3.22400 \\ Ga_2 & = 3.99063 \\ Ga_3 & = 4.80299 \\ Ga_4 & = 9.78188e-1 \\ Ga_5 & = 1.71069 \\ Gb_0 & = -6.24097e-3 \\ Gb_1 & = -6.93498e-3 \\ Gb_2 & = -6.90358e-3 \\ Gb_3 & = -4.29155e-3 \\ Gc_0 & = -3.11680e-7 \end{aligned} \end{equation*}\end{array} //]]>$

Air vapour pressure (in dbar) is calculated as:

$//<![CDATA[ \begin{array}{l}Pav = \dfrac{exp(52.57 - \dfrac{6690.9}{T + 273.15} - 4.6818 \cdot ln(T + 273.15))}{100}\end{array} //]]>$