F.1 Sediment ammonium and nitrate flux

Ammonium and nitrate are exchanged between the water column and sediments via specification of separate sediment fluxes. In both cases, this flux is most commonly out of the sediments, i.e. a positive specification of sediment flux. Although it is rare that sediments act as sinks of these nitrogenous species, the WQ Module can be parameterised to allow for this if required.

The user specified rates of ammonium and nitrate fluxes (which can be spatially varying) are modified by overlying ambient dissolved oxygen concentration (together with respective user specified half saturation oxygen concentrations) and water temperature. These modifications are simulated via Michaelis-Menten and Arrhenius models, respectively, as per Equation (F.1). \[\begin{equation} \left.\begin{aligned} \href{AppDiags.html#WQDiagAmmSedFlx}{F_{sed\langle computed\rangle}^{NH_4}} =& F_{sed}^{NH_4} \times \frac{K_{sed-O_2}^{NH_4}}{K_{sed-O_2}^{NH_4} + \left[DO\right]} \times \hphantom{\text{ab}} \left[\theta_{sed}^{NH_4}\right]^{\left(T-20\right)} \\ \\ \href{AppDiags.html#WQDiagNitSedFlx}{F_{sed\langle computed\rangle}^{NO_3}} =& F_{sed}^{NO_3} \times \underbrace{\frac{\left[DO\right]}{K_{sed-O_2}^{NO_3} + \left[DO\right]}}_{\text{Influence of oxygen}} \times \underbrace{\vphantom{\frac{\left[DO\right]}{K_{sed-O_2}^{NO_3} + \left[DO\right]}} \left[\theta_{sed}^{NO_3}\right]^{\left(T-20\right)}}_{\text{Influence of temperature}} \end{aligned}\right\} \tag{F.1} \end{equation}\] \(F_{sed}^{NH_4}\) and \(F_{sed}^{NO_3}\) are the user specified ammonium and nitrate sediment fluxes at 20\(^o\)C without the influence of dissolved oxygen, \(\left[DO\right]\) is the overlying dissolved oxygen concentration, \(K_{sed-O_2}^{NH_4}\) and \(K_{sed-O_2}^{NO_3}\) are the user specified half saturation concentrations of dissolved oxygen for ammonium and nitrate sediment flux, \(\theta_{sed}^{NH_4}\) and \(\theta_{sed}^{NO_3}\) are the corresponding temperature coefficients, and \(T\) is ambient water temperature.

As per silicate sediment flux (see Section E.1), the above equations lead to linearly varying ambient ammonium and nitrate concentrations in the demonstration model when dissolved oxygen concentration, half saturation oxygen concentrations and ambient temperature are set to be constant.

A more realistic environmental setting has sediment ammonium and nitrate fluxes occurring against a background of oxygen concentration drawdown. The demonstration model has been used to illustrate this via execution of a suite of simulations that experience dissolved oxygen drawdown (in the dissolved oxygen constituent model, with \(K_{sed-O_2}^{O_2}\) = 4 mg/L) and each simulation using a the same value for both \(K_{sed-O_2}^{NH_4}\) and \(K_{sed-O_2}^{NO_3}\). The ammonium and nitrate sediment flux rates were both specified as 140 mg/m\(^2\)/d, and temperature effects were turned off. The predicted temporal evolution of water column ammonium and nitrate concentrations is provided in Figure F.1. Use the “play” button or drag the slider to see how different half saturation concentrations change ambient concentrations (ordinate) in time (abscissa).

Figure F.1: Move the slider to see the effect of changing the \(K_{sed-O_2}^{NH_4}\) (and \(K_{sed-O_2}^{NO_3}\) - they are set to be equal to each other in this example) values on ambient ammonium and nitrate concentrations. Ambient dissolved oxygen is drawn down in time

Figure F.1 illustrates the different oxygen responses of ammonium and nitrate sediment fluxes, as reflected in the different formulations within Equation (F.1). Importantly, the figure demonstrates that as ambient oxygen concentrations reach zero near 60 hours (see Figure D.2 with the slider bar set to \(K_{sed-O_2}^{O_2}\) = 4 mg/L), nitrate sediment flux ceases and the resultant ambient concentrations plateau. The converse is true to ammonium. One implication of this behaviour is that in environmental systems being simulated using the WQ Module, the rate of delivery of ammonium mass to the water column will generally increase under low dissolved oxygen conditions (e.g. waters isolated underneath a strong lacustrine a thermocline), whilst the corresponding nitrate mass fluxes will reduce under the same conditions. This is the expected and observed behaviour of environmental systems.

The rate of ammonium and nitrate flux is also related to ambient water temperature, via the Arrhenius model in Equation (F.1). To demonstrate this, the same model above (with time varying dissolved oxygen concentration) was executed at a range of ambient temperatures, but constant half saturation concentrations for oxygen for both ammonium and nitrate set to 4 mg/L. All temperature coefficients were set to 1.05. The results are provided in Figure F.2. Use the “play” button or drag the slider to see how different ambient temperatures change the ambient ammonium and nitrate concentrations (ordinate) in time (abscissa).

Figure F.2: Move the slider to see the effect of changing the ambient water temperature on ammonium and nitrate concentrations, with ambient dissolved oxygen drawdown

The figure shows that as ambient water temperature increases, the rate of increases of both ammonium and nitrate concentrations follow suit. Again, nitrate concentrations plateau once background dissolved oxygen concentrations reach zero, however ammonium concentrations continue to rise throughout the simulation. This is expected behaviour.