Appendix D Processes: oxygen

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 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.

D.2 Sediment oxygen flux

Oxygen is exchanged between the water column and sediments via specification of a sediment flux representing the net effect of biological activity. In the case of oxygen, this flux is most commonly into the sediments, i.e. a negative sediment flux. Although it is rare that sediments act as sources of oxygen, the WQ Module can be parameterised to allow for this if required.

The user specified sediment oxygen flux (which can be spatially varying) is modified by overlying ambient dissolved oxygen concentration (together with a user specified half saturation oxygen concentration) and water temperature. These modifications are simulated via Michaelis-Menten and Arrhenius models, respectively, as per Equation (D.6). \[\begin{equation} \href{AppDiags.html#WQDiagDOSedFlx}{F_{sed\langle computed\rangle}^{O_2}} = F_{sed}^{O_2} \times \underbrace{\frac{\left[DO\right]}{K_{sed-O_2}^{O_2} + \left[DO\right]}}_{\text{Influence of oxygen}} \times \underbrace{ \vphantom{ \frac{\left[DO\right]}{K_{sed-O_2}^{O_2} + \left[DO\right]} } \left[\theta_{sed}^{O_2}\right]^{\left(T-20\right)}}_{\text{Influence of temperature}} \tag{D.6} \end{equation}\] \(F_{sed}^{O_2}\) is the user specified oxygen sediment flux at 20\(^o\)C without the influence of dissolved oxygen, \(\left[DO\right]\) is the overlying dissolved oxygen concentration computed by the WQ Module, \(K_{sed-O_2}^{O_2}\) and \(\theta_{sed}^{O_2}\) are the half saturation oxygen concentration and temperature coefficient for dissolved oxygen sediment flux respectively, and \(T\) is ambient water temperature.

The form of the above relationship between dissolved oxygen concentration and the computed oxygen sediment flux, for a range of \(K_{sed-O_2}^{O_2}\) values is provided in Figure D.1. Water temperature is held constant at 20\(^o\)C and \(\theta_{sed}^{O_2}=1\) (i.e. the Arrhenius temperature function is switched off). The user specified benthic oxygen sediment flux is -4,800 mg/m\(^2\)/day. Use the “play” button or drag the slider to see how different half saturation oxygen concentrations change the oxygen sediment flux (ordinate), as a function of ambient dissolved oxygen concentration (abscissa).

Figure D.1: Move the slider to see the effect of changing \(K_{sed-O_2}^{O_2}\) on the computed oxygen sediment flux

The figure demonstrates that in this example, the smaller the value of \(K_{sed-O_2}^{O_2}\), the faster the magnitude of the computed oxygen sediment flux increases with ambient dissolved oxygen concentration. This is consistent with one interpretation of \(K_{sed-O_2}^{O_2}\), that it is the ambient dissolved oxygen concentration at which the computed oxygen sediment flux is half that of the user specified \(F_{sed}^{O_2}\), when temperature effects are turned off.

In light of the above, the demonstration model has been used to illustrate the influence that the half saturation concentration has on the rate of drawdown of water column dissolved oxygen. The model was repeatedly executed using a different \(K_{sed-O_2}^{O_2}\) for each simulation, but at the same water temperature of (approximately) 20\(^o\)C, and with temperature effects turned off. The predicted temporal evolution of water column dissolved oxygen concentration is provided in Figure D.2. Use the “play” button or drag the slider to see how different half saturation oxygen concentrations change the rate of dissolved oxygen (ordinate) drawdown with time (abscissa).

Figure D.2: Move the slider to see the effect of changing \(K_{sed-O_2}^{O_2}\) on the rate of consumption of dissolved oxygen in water immediately above the sediments

Consistent with the behaviour demonstrated in Figure D.1, Figure D.2 has a less rapid drawdown of ambient dissolved oxygen concentrations with increasing \(K_{sed-O_2}^{O_2}\).

The rate of dissolved oxygen drawdown is also related to ambient water temperature, via the Arrhenius model in Equation (D.6). To illustrate this, the demonstration model was executed at a range of ambient temperatures, a constant half saturation oxygen concentration for oxygen sediment flux of 4 mg/L and a temperature factor \(\theta_{sed}^{O_2}\) of 1.05. The results are provided in Figure D.3. Use the “play” button or drag the slider to see how different ambient temperatures change the rate of dissolved oxygen (ordinate) drawdown under these conditions, with time (abscissa).

Figure D.3: Move the slider to see the effect of changing the ambient water temperature on dissolved oxygen concentrations

The figure confirms the expected result that the rate of dissolved oxygen drawdown increases with increasing ambient water temperature. This increased rate reflects the expected increase in benthic biological activity with temperature.