N.4 Mineralisation

Mineralisation is the pelagic biological conversion of labile dissolved organic matter to dissolved inorganic carbon and nutrients. It is therefore a source of dissolved inorganic carbon, ammonium and filterable reactive phosphorus, and a sink of the corresponding labile dissolved organics. Mineralisation is conceptualised as comprising aerobic (i.e. consuming dissolved oxygen and (via denitrification) inorganic nitrate) and anaerobic components, and is implemented within the labile organics constituent model of the WQ Module. The term organic matter in this section therefore refers to labile organic matter.

The same pelagic mineralisation rate is computed within the WQ Module for dissolved organic carbon, nitrogen and phosphorus via Equation (N.8). \[\begin{equation} R_{miner\langle computed\rangle}^{DOM} = R_{miner}^{DOM} \times \underbrace{\left[\underbrace{\frac{\left[DO\right]}{K_{miner-O_2}^{DOM} + \left[DO\right]}}_{\text{O2 consumption}} + \underbrace{f_{an} \times \frac{K_{miner-O_2}^{DOM}}{K_{miner-O_2}^{DOM} + \left[DO\right]}}_{\text{non-O2 consumption}}\right]}_{\text{Influence of oxygen}} \times \underbrace{\vphantom{\left[\underbrace{\frac{\left[DO\right]}{K_{miner-O_2}^{DOM} + \left[DO\right]}}_{\text{aerobic}} + \underbrace{f_{an} \times \frac{K_{miner-O_2}^{DOM}}{K_{miner-O_2}^{DOM} + \left[DO\right]}}_{\text{anaerobic}}\right]} \hphantom{\text{ab}} \left[\theta_{miner}^{DOM}\right]^{\left(T-20\right)}}_{\text{Influence of temperature}} \tag{N.8} \end{equation}\] \(R_{miner}^{DOM}\) is the user specified (or default) dissolved organic matter (i.e. carbon, nitrogen and phosphorus) mineralisation rate at 20\(^o\)C without the influence of dissolved oxygen, \(\left[DO\right]\) is the ambient dissolved oxygen concentration, \(K_{miner-O_2}^{DOM}\) is the user specified half saturation concentration of dissolved oxygen for dissolved organic matter mineralisation, \(\theta_{miner}^{DOM}\) is the corresponding temperature coefficient, \(f_{an}\) is a fractional multiplier that weights the Michaelis-Menten contribution of non-O\(_2\) processes within the calculation of total mineralisation and \(T\) is ambient water temperature. As per sediment fluxes and hydrolysis, the values of \(K_{miner-O_2}^{DOM}\) and \(\theta_{miner}^{DOM}\) are intentionally applied equally to dissolved organic carbon, nitrogen and phosphorus mineralisation. In addition, the rate at which mineralisation of dissolved organic matter (to inorganics) occurs is the same for all dissolved organic constituents. This is because there is one (not three) biological conversion process that is assumed to draw equally on all dissolved organic constituents. Finally, setting \(f_{an}\) to zero does not suppress entirely non-O\(_2\) mineralisation (see following section), but it does remove the Michaelis-Menten based influence of anaerobic processes on the calculation of total mineralisation.

N.4.1 Consumption

The mineralisation rate from Equation (N.8) is multiplied by ambient labile dissolved organic carbon, nitrogen and phosphorus concentrations to compute their respective consumptive fluxes (losses) at each model timestep in each model cell via Equation (N.9).

\[\begin{equation} \left.\begin{aligned} \href{AppDiags.html#WQDiagDOCMiner}{F_{miner\langle computed\rangle}^{DOC}} =& R_{miner\langle computed\rangle}^{DOM} \times \left[ DOC \right] \\ \\ \href{AppDiags.html#WQDiagDONMiner}{F_{miner\langle computed\rangle}^{DON}} =& R_{miner\langle computed\rangle}^{DOM} \times \left[ DON \right] \\ \\ \href{AppDiags.html#WQDiagDOPMiner}{F_{miner\langle computed\rangle}^{DOP}} =& R_{miner\langle computed\rangle}^{DOM} \times \left[ DOP \right] \end{aligned}\right\} \tag{N.9} \end{equation}\]

The fraction of dissolved organic carbon mineralisation that consumes dissolved oxygen \(O_2\) is given by Equation (N.10). \(K_{miner-O_2}^{DOM}\), \(\left[DO\right]\) and \(f_{an}\) have been described previously.

\[\begin{equation} f_{miner-O_2\langle computed\rangle}^{DOC} = \frac{\frac{\left[DO\right]}{K_{miner-O_2}^{DOM} + \left[DO\right]}}{\frac{\left[DO\right]}{K_{miner-O_2}^{DOM} + \left[DO\right]} + f_{an} \times \frac{K_{miner-O_2}^{DOM}}{K_{miner-O_2}^{DOM} + \left[DO\right]}} \tag{N.10} \end{equation}\]

Applying a 1:1 molar ratio of mineralised dissolved organic carbon to consumed diatomic dissolved oxygen, gives the consumptive oxygen flux \(F_{miner\langle computed\rangle}^{O_2}\) as:

\[\begin{equation} F_{miner\langle computed\rangle}^{O_2} = F_{miner\langle computed\rangle}^{DOC} \times f_{miner-O_2\langle computed\rangle}^{DOC} \tag{N.11} \end{equation}\]

Substituting Equations (N.8) and (N.9) into Equation (N.11) and cancelling terms gives the final expression for \(F_{miner\langle computed\rangle}^{O_2}\) as Equation (N.12), again with parameters described previously.

\[\begin{equation} F_{miner\langle computed\rangle}^{O_2} = F_{miner\langle computed\rangle}^{DOC} \times \frac{\left[DO\right]}{K_{miner-O_2}^{DOM} + \left[DO\right]} \tag{N.12} \end{equation}\]

This is also expressed as the reduction of ambient dissolved oxygen concentration that would result from this consumptive mineralisation over a period of five days. It is a common laboratory reporting unit and referred to as BOD5 (biological oxygen demand over 5 days). BOD5 is computed as per Equation (N.13). \[\begin{equation} \href{AppDiags.html#WQDiagDOCBDO5}{BOD5_{\langle computed\rangle}^{O_2}} = F_{miner\langle computed\rangle}^{O_2} \times 5 \tag{N.13} \end{equation}\]

A portion of remaining mineralisation (\(F_{miner\langle computed\rangle}^{DOC} - F_{miner\langle computed\rangle}^{O_2}\)) flux (that follows dissolved oxygen consumption) sources its oxygen from ambient nitrate. This consumptive flux of nitrate \(F_{miner\langle computed\rangle}^{NO_3}\) is referred to as denitrification and is the reduction of nitrate N to free diatomic nitrogen gas. Again applying a 1:1 molar ratio of consumed dissolved organic carbon to nitrate, this is quantity is computed via Equation (N.14).

\[\begin{equation} \href{AppDiags.html#WQDiagDOCDenitrif}{F_{miner\langle computed\rangle}^{NO_3}} = \left(F_{miner\langle computed\rangle}^{DOC} - F_{miner\langle computed\rangle}^{O_2}\right) \times \frac{\left[NO_3\right]}{K_{miner-NO_3}^{NO_3} + \left[NO_3\right]} \tag{N.14} \end{equation}\] \(K_{miner-NO_3}^{NO_3}\) is the user specified half saturation concentration of nitrate for consumption of nitrate as result of mineralisation of dissolved organic carbon and \(\left[NO_3\right]\) is the ambient nitrate concentration.

The remaining dissolved organic carbon mineralisation flux is referred to as anaerobic mineralisation, \(F_{miner\langle computed\rangle}^{an}\), such that the following overall molar equality applies (with \(O2\) and \(NO_3\) being in a 1:1 molar ration with their respective carbon fluxes):

\[\begin{equation} F_{miner\langle computed\rangle}^{DOC} = F_{miner\langle computed\rangle}^{O_2} + F_{miner\langle computed\rangle}^{NO_3} + \href{AppDiags.html#WQDiagDOCAnMiner}{F_{miner\langle computed\rangle}^{an}} \tag{N.15} \end{equation}\]

In summary:

• \(F_{miner\langle computed\rangle}^{DOC}\) is the total mineralisation flux of DOC to dissolved inorganics
• \(F_{miner\langle computed\rangle}^{O_2}\) is the portion of the total mineralisation flux that uses dissolved oxygen as its oxygen source. The flux of DOC and dissolved oxygen are applied as a 1:1 molar ratio
• \(F_{miner\langle computed\rangle}^{NO_3}\) is the portion of the total mineralisation flux that uses nitrate as its oxygen source. The flux of DOC and nitrate are applied as a 1:1 molar ratio
• \(F_{miner\langle computed\rangle}^{an}\) is the remaining portion of the total mineralisation flux that uses no oxygen. It consumes no computed variables other than DOC

All these mineralisation diagnostic variables are reported in units of carbon.

N.4.2 Production

The consumptive flux from Equation (N.6) results in the inorganic carbon, ammonium and FRP productive fluxes in Equation (N.16).

\[\begin{equation} \left.\begin{aligned} F_{miner\langle computed\rangle}^{DIC} =& F_{miner\langle computed\rangle}^{DOC} \\ \\ F_{miner\langle computed\rangle}^{NH_4} =& F_{miner\langle computed\rangle}^{DON} \\ \\ F_{miner\langle computed\rangle}^{FRP} =& F_{miner\langle computed\rangle}^{DOP} \end{aligned}\right\} \tag{N.16} \end{equation}\]

The WQ Module does not currently support simulation of dissolved inorganic carbon (DIC) so the corresponding carbonic productive flux in Equation (N.16) has no effect on inorganic water quality dynamics. Contact support@tuflow.com if the DIC model is required.