G.1 Sediment FRP flux

Filterable reactive phosphorus (FRP) is exchanged between the water column and sediments via specification of sediment fluxes. 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 FRP, WQ Module can be parameterised to allow for this if required.

The user specified rate of FRP 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 (G.1). \[\begin{equation} \href{AppDiags.html#WQDiagFRPSedFlx}{F_{sed\langle computed\rangle}^{FRP}} = F_{sed}^{FRP} \times \underbrace{\frac{K_{sed-O_2}^{FRP}}{K_{sed-O_2}^{FRP} + \left[DO\right]}}_{\text{Influence of oxygen}} \times \underbrace{\vphantom{\frac{K_{sed-O_2}^{FRP}}{K_{sed-O_2}^{FRP} + \left[DO\right]}} \left[\theta_{sed}^{FRP}\right]^{\left(T-20\right)}}_{\text{Influence of temperature}} \tag{G.1} \end{equation}\] \(F_{sed}^{FRP}\) is the user specified FRP sediment flux at 20\(^o\)C without the influence of dissolved oxygen, \(\left[DO\right]\) is the overlying dissolved oxygen concentration, \(K_{sed-O_2}^{FRP}\) is the user specified half saturation concentration of dissolved oxygen for FRP sediment flux, \(\theta_{sed}^{FRP}\) is the corresponding temperature coefficient, and \(T\) is ambient water temperature.

As per silicate sediment fluxes (see Section E.1), the above equation leads to linearly varying ambient FRP concentrations in the demonstration model when dissolved oxygen concentration, half saturation oxygen concentration and temperature are set to be constant.

A more realistic environmental setting has sediment FRP flux 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, with \(K_{sed-O_2}^{O_2}\) = 4 mg/L and each simulation using a different \(K_{sed-O_2}^{FRP}\). The FRP sediment flux rate was specified as 400 mg/m\(^2\)/d and temperature effects were turned off. The predicted temporal evolution of water column FRP concentrations is provided in Figure G.1. Use the “play” button or drag the slider to see how different half saturation concentrations change ambient concentrations.

Figure G.1: Move the slider to see the effect of changing the \(K_{sed-O_2}^{FRP}\) values on ambient FRP concentrations. Ambient dissolved oxygen is drawn down in time

The rate of FRP flux is also related to ambient water temperature, via the Arrhenius model in Equations (G.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 set to 4 mg/L. All temperature coefficients were set to 1.05. The results are provided in Figure G.2. Use the “play” button or drag the slider to see how different ambient temperatures change ambient concentrations.

Figure G.2: Move the slider to see the effect of changing the ambient water temperature on the rate of FRP fluxes to water immediately above the sediments, with ambient dissolved oxygen drawdown

The figure shows that as ambient water temperature increases, the rate of increase of FRP concentrations follow suit. This is expected behaviour.