N.1 Sediment flux

Dissolved organic carbon, nitrogen and phosphorus are exchanged between the water column and sediments via specification of separate sediment fluxes. In all 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 species, TUFLOW WQ Module can be parameterised to allow for this if required. Only labile dissolved organic matter is released from the sediments in the WQ Module, and as such, references to organics in this section should be interpreted as labile organics.

The user specified rates of dissolved organic 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 (N.1). \[\begin{equation} \left.\begin{aligned} \href{AppDiags.html#WQDiagDOCSedFlx}{F_{sed\langle computed\rangle}^{DOC}} =& F_{sed}^{DOC} \times \frac{K_{sed-O_2}^{DOM}}{K_{sed-O_2}^{DOM} + \left[DO\right]} \times \hphantom{\text{ab}} \left[\theta_{sed}^{DOM}\right]^{\left(T-20\right)} \\ \\ \href{AppDiags.html#WQDiagDONSedFlx}{F_{sed\langle computed\rangle}^{DON}} =& F_{sed}^{DON} \times \frac{K_{sed-O_2}^{DOM}}{K_{sed-O_2}^{DOM} + \left[DO\right]} \times \hphantom{\text{ab}} \left[\theta_{sed}^{DOM}\right]^{\left(T-20\right)} \\ \\ \href{AppDiags.html#WQDiagDOPSedFlx}{F_{sed\langle computed\rangle}^{DOP}} =& F_{sed}^{DOP} \times \underbrace{\frac{K_{sed-O_2}^{DOM}}{K_{sed-O_2}^{DOM} + \left[DO\right]}}_{\text{Influence of oxygen}} \times \underbrace{\vphantom{\frac{\left[DO\right]}{K_{sed-O_2}^{NO_3} + \left[DO\right]}} \left[\theta_{sed}^{DOM}\right]^{\left(T-20\right)}}_{\text{Influence of temperature}} \end{aligned}\right\} \tag{N.1} \end{equation}\] \(F_{sed}^{DOC}\), \(F_{sed}^{DON}\) and \(F_{sed}^{DOP}\) are the user specified dissolved organic carbon, nitrogen and phosphorus sediment fluxes at 20\(^o\)C without the influence of dissolved oxygen, \(\left[DO\right]\) is the overlying dissolved oxygen concentration, \(K_{sed-O_2}^{DOM}\) is the user specified half saturation concentration of dissolved oxygen for dissolved organic matter sediment flux, \(\theta_{sed}^{DOM}\) is the corresponding temperature coefficient, and \(T\) is ambient water temperature. The values of \(K_{sed-O_2}^{DOM}\) and \(\theta_{sed}^{DOM}\) are intentionally applied equally to dissolved organic carbon, nitrogen and phosphorus sediment fluxes. This is because there is one (not three) biological consumption process that generates these constituents: \(K_{sed-O_2}^{DOM}\) and \(\theta_{sed}^{DOM}\) apply to this single process. In a similar vein, the user specifications for \(F_{sed}^{DOC}\), \(F_{sed}^{DON}\) and \(F_{sed}^{DOP}\) should not vary significantly in their relative proportions from the ratio that these typically occur in the organic matter being consumed (e.g. the Redfield ratio).

As per silicate sediment flux (see Section E.1), the above equations lead to linearly varying ambient dissolved organics concentrations in the demonstration model when dissolved oxygen concentration, half saturation oxygen concentrations and ambient temperature are set to be constant. As per FRP simulation, the above equations also lead to the form of sediment release presented in Figures G.1 and G.2 when oxygen drawdown and temperature changes occur, respectively.