D.1 Atmospheric oxygen flux

Atmospheric oxygen flux is a key source of water column dissolved oxygen. Oxygenation is implemented in the upper model layer by the WQ Module, and then this oxygenated water is mixed downwards by TUFLOW in subsequent timesteps.

Initially, a Schmidt number \(Sc_{atm}^{O_2}\) is computed via Equation (D.1).

\[\begin{equation} Sc_{atm}^{O_2} = \left(0.9 + \frac{S}{350.0}\right)\times\left(2073.1-125.62T+3.6276T^2-0.043219T^3\right) \tag{D.1} \end{equation}\]

\(T\) and \(S\) are ambient water temperature and salinity respectively. An oxygen piston velocity \(V_{pist}^{O_2}\) (also known as a gas transfer velocity) is then computed. Two piston models for \(V_{pist}^{O_2}\) are available. The first is due to Wanninkhof (1992):

\[\begin{equation} V_{pist}^{O_2} = 0.31 \left( V_{wind}^{O_2} \right) ^2 \times \left(\frac{660.0}{Sc_{atm}^{O_2}}\right)^x \tag{D.2} \end{equation}\]

where \(V_{wind}^{O_2}\) is wind speed. For wind speed \(V_{wind}^{O_2}\)<3.0 m/s, \(x\) is 0.66, otherwise \(x\) is 0.5. Wind speed is assumed to be provided from TUFLOW at 10 metres from the water surface. The second is due to Ho et al. (2016):

\[\begin{equation} V_{pist}^{O_2} = \left(0.77 \sqrt{\frac{V_{water}}{H_{layer}}} + 0.266 \left(V_{wind}^{O_2} \right) ^2\right) \times \sqrt{\frac{660.0}{Sc_{atm}^{O_2}}} \tag{D.3} \end{equation}\]

where \(V_{water}\) is surface water speed, \(H_{layer}\) is the thickness of the uppermost TUFLOW FV computational layer and \(V_{wind}^{O_2}\) is wind speed.

There are other models available for computing both \(Sc_{atm}^{O_2}\) and \(V_{pist}^{O_2}\) within the WQ Module. Contact support@tuflow.com if these are required.

Once \(Sc_{atm}^{O_2}\) and \(V_{pist}^{O_2}\) are known, oxygenation to the surface layer is computed as per Equation (D.4). \[\begin{equation} \href{AppDiags.html#WQDiagDOAtmFlx}{F_{atm}^{O_2}} = V_{pist}^{O_2} \left(\left[DO\right]_{air} - \left[DO\right]\right) \tag{D.4} \end{equation}\] \(F_{atm}^{O_2}\) is the flux of atmospheric oxygen to the surface layer, and \(\left[DO\right]_{air}\) and \(\left[DO\right]\) are the oxygen concentrations in air and water (as a computed variable in a computational cell) at the air-water interface, respectively. \(\left[DO\right]_{air}\) is assumed to be the saturation concentration of dissolved oxygen in water which is at the ambient surface water’s temperature and salinity conditions. As such, supersaturated surface waters will release dissolved oxygen to the atmosphere under this schematisation. Oxygen percent saturation is computed as per Equation (D.5).

\[\begin{equation} \left.\begin{aligned} \left[DO\right]_{psat} =& 100.0 \times \frac{\left[DO\right]}{\left[DO\right]_{sat}} \\ \\ \href{AppDiags.html#WQDiagDOSat}{\left[DO\right]_{sat}} =& 1.42763 \times e^{C} \\ \\ C =& -173.4292 + \left(249.6339 \times \frac{100.0}{T+273.15}\right) + \left(143.3483 \times \ln\left(\frac{T+273.15}{100.0}\right)\right) \ldots \\ & \left(-21.8492 \times \frac{T+273.15}{100.0}\right) \ldots \\ & - S \times \left(-0.033096 + \left(0.014259 \times \frac{T+273.15}{100.0}\right) - 0.0017 \times \left(\frac{T+273.15}{100.0}\right)^{2.0}\right) \end{aligned}\right\} \tag{D.5} \end{equation}\] \(T\) and \(S\) are ambient water temperature and salinity respectively.