Appendix N Processes: organic matter

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.

N.2 Hydrolysis

Hydrolysis is the pelagic biological conversion of labile particulate organic matter to labile dissolved organic matter. It is therefore a source of dissolved carbon, nitrogen and phosphorus, and a sink of the corresponding particulates. Hydrolysis neither consumes or produces dissolved oxygen or bioavailable inorganic nutrients. Hydrolysis is implemented within the labile organics constituent model of the WQ Module, and the term organic matter in this section therefore refers to labile organic matter. Refractory organic matter processes are described elsewhere.

The pelagic hydrolysis rate is computed within the labile organics constituent model via Equation (N.2).

\[\begin{equation} \left.\begin{aligned} R_{hyd\langle computed\rangle}^{POC} =& R_{hyd}^{POC} \times \frac{\left[DO\right]}{K_{hyd-O_2}^{POM} + \left[DO\right]} \times \hphantom{\text{ab}} \left[\theta_{hyd}^{POM}\right]^{\left(T-20\right)} \\ \\ R_{hyd\langle computed\rangle}^{PON} =& R_{hyd}^{PON} \times \frac{\left[DO\right]}{K_{hyd-O_2}^{POM} + \left[DO\right]} \times \hphantom{\text{ab}} \left[\theta_{hyd}^{POM}\right]^{\left(T-20\right)} \\ \\ R_{hyd\langle computed\rangle}^{POP} =& R_{hyd}^{POP} \times \underbrace{\frac{\left[DO\right]}{K_{hyd-O_2}^{POM} + \left[DO\right]}}_{\text{Influence of oxygen}} \times \underbrace{\vphantom{\frac{\left[DO\right]}{K_{sed-O_2}^{NO_3} + \left[DO\right]}} \hphantom{\text{ab}} \left[\theta_{hyd}^{POM}\right]^{\left(T-20\right)}}_{\text{Influence of temperature}} \end{aligned}\right\} \tag{N.2} \end{equation}\] \(R_{hyd}^{POC}\), \(R_{hyd}^{PON}\) and \(R_{hyd}^{POP}\) are the user specified particulate organic carbon, nitrogen and phosphorus hydrolysis rates at 20\(^o\)C without the influence of dissolved oxygen, \(\left[DO\right]\) is the ambient dissolved oxygen concentration, \(K_{hyd-O_2}^{POM}\) is the user specified half saturation concentration of dissolved oxygen for particulate organic matter hydrolysis, \(\theta_{hyd}^{POM}\) is the corresponding temperature coefficient, and \(T\) is ambient water temperature. As per sediment fluxes, the values of \(K_{hyd-O_2}^{POM}\) and \(\theta_{hyd}^{POM}\) are intentionally applied equally to particulate organic carbon, nitrogen and phosphorus hydrolysis. This is because there is one (not three) biological consumption process that generates these constituents: \(K_{hyd-O_2}^{POM}\) and \(\theta_{hyd}^{POM}\) apply to this single process. In a similar vein, the user specifications for \(R_{hyd}^{POC}\), \(R_{hyd}^{PON}\) and \(R_{hyd}^{POP}\) 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).

N.2.1 Consumption

The hydrolysis rates from Equation (N.2) are multiplied by their respective ambient particulate organic matter concentrations to compute their respective consumptive fluxes (losses) at each model timestep in each model cell via Equation (N.3).

\[\begin{equation} \left.\begin{aligned} \href{AppDiags.html#WQDiagPOCHydrol}{F_{hyd\langle computed\rangle}^{POC}} =& R_{hyd\langle computed\rangle}^{POC} \times \left[ POC \right] \\ \\ \href{AppDiags.html#WQDiagPONHydrol}{F_{hyd\langle computed\rangle}^{PON}} =& R_{hyd\langle computed\rangle}^{PON} \times \left[ PON \right] \\ \\ \href{AppDiags.html#WQDiagPOPHydrol}{F_{hyd\langle computed\rangle}^{POP}} =& R_{hyd\langle computed\rangle}^{POP} \times \left[ POP \right] \end{aligned}\right\} \tag{N.3} \end{equation}\]

N.2.2 Production

The consumptive fluxes from Equation (N.3) result in the dissolved organic productive fluxes in Equation (N.4).

\[\begin{equation} \left.\begin{aligned} F_{hyd\langle computed\rangle}^{DOC} =& F_{hyd\langle computed\rangle}^{POC} \\ \\ F_{hyd\langle computed\rangle}^{DON} =& F_{hyd\langle computed\rangle}^{PON} \\ \\ F_{hyd\langle computed\rangle}^{DOP} =& F_{hyd\langle computed\rangle}^{POP} \end{aligned}\right\} \tag{N.4} \end{equation}\]

N.3 Breakdown

Breakdown is the pelagic biological conversion of refractory particulate organic matter (which is a single computed variable) to three labile particulate organic matter computed variables. It is therefore a source of labile particulate organic carbon, nitrogen and phosphorus, and a sink of refractory particulate organic matter. Breakdown neither consumes or produces dissolved oxygen or bioavailable inorganic nutrients. Breakdown is implemented within the refractory organics constituent model of the WQ Module only, so the following does not apply if the labile organics constituent model is used.

The pelagic breakdown rate of refractory particulate organic matter is computed via Equation (N.5).

\[\begin{equation} R_{bdn\langle computed\rangle}^{RPOM} = R_{bdn}^{RPOM} \times \underbrace{\frac{\left[DO\right]}{K_{hyd-O_2}^{POM} + \left[DO\right]}}_{\text{Influence of oxygen}} \times \underbrace{\vphantom{\frac{\left[DO\right]}{K_{sed-O_2}^{NO_3} + \left[DO\right]}} \hphantom{\text{ab}} \left[\theta_{hyd}^{POM}\right]^{\left(T-20\right)}}_{\text{Influence of temperature}} \tag{N.5} \end{equation}\] \(R_{bdn}^{RPOM}\)is the user specified (or default) refractory particulate organic matter breakdown rate at 20\(^o\)C without the influence of dissolved oxygen, \(\left[DO\right]\) is the ambient dissolved oxygen concentration, \(K_{hyd-O_2}^{POM}\) is the user specified (or default) half saturation concentration of dissolved oxygen for labile particulate organic matter hydrolysis, \(\theta_{hyd}^{POM}\) is the corresponding temperature coefficient, and \(T\) is ambient water temperature. The parameters \(K_{hyd-O_2}^{POM}\) and \(\theta_{hyd}^{POM}\) used in Equation (N.5) are the same as those used for the hydrolysis calculations described in Section N.2 and specified via the associated labile organic matter hydrolysis command.

N.3.1 Consumption

The breakdown rate from Equation (N.5) is multiplied by the ambient refractory particulate organic matter concentration to compute its consumptive flux (loss) at each model timestep in each model cell via Equation (N.6).

\[\begin{equation} \href{AppDiags.html#WQDiagBdn}{F_{bdn\langle computed\rangle}^{RPOM}} = R_{bdn\langle computed\rangle}^{RPOM} \times \left[ RPOM \right] \tag{N.6} \end{equation}\]

N.3.2 Production

The consumptive flux from Equation (N.6) results in the labile particulate organic carbon, nitrogen and phosphorus productive fluxes in Equation (N.7).

\[\begin{equation} \left.\begin{aligned} F_{bdn\langle computed\rangle}^{POC} =& F_{bdn\langle computed\rangle}^{RPOM} \\ \\ F_{bdn\langle computed\rangle}^{PON} =& F_{bdn\langle computed\rangle}^{RPOM} \times X_N^{RPOM} \\ \\ F_{bdn\langle computed\rangle}^{POP} =& F_{bdn\langle computed\rangle}^{RPOM} \times X_P^{RPOM} \end{aligned}\right\} \tag{N.7} \end{equation}\] \(X_N^{RPOM}\) and \(X_P^{RPOM}\) are the user specified (or default) molar ratios of nitrogen and phosphorus to carbon within refractory particulate organic matter. These should not differ significantly from the Redfield ratios of 16/106 and 1/106, respectively.

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.

N.5 Activation

Activation is the pelagic biological conversion of refractory dissolved organic carbon, nitrogen and phosphorus to their respective labile dissolved organic equivalents. It is therefore a source of dissolved labile organic carbon, nitrogen and phosphorus, and a sink of the corresponding refractory dissolved organics. Activation does not consume or produce any other computed variables, although its computed rate does depend on dissolved oxygen concentration.

The pelagic activation rate is computed within the WQ Module for refractory dissolved organic carbon, nitrogen and phosphorus via Equation (N.17).

\[\begin{equation} R_{act\langle computed\rangle}^{RDOM} = R_{act}^{RDOM} \times \underbrace{\left[\underbrace{\frac{\left[DO\right]}{K_{miner-O_2}^{DOM} + \left[DO\right]}}_{\text{aerobic}} + \underbrace{f_{an} \times \frac{K_{miner-O_2}^{DOM}}{K_{miner-O_2}^{DOM} + \left[DO\right]}}_{\text{anaerobic}}\right]}_{\text{Influence of oxygen}} \times \underbrace{\vphantom{\left[\underbrace{\frac{\left[DO\right]}{K_{miner-O_2}^{DOM} + \left[DO\right]}}_{\text{aerobic}} + \underbrace{f_{an} \times \frac{K_{miner-O_2}^{DOM}}{K_{miner-O_2}^{DOM} + \left[DO\right]}}_{\text{anaerobic}}\right]} \hphantom{\text{ab}} \left[\theta_{miner}^{DOM}\right]^{\left(T-20\right)}}_{\text{Influence of temperature}} \tag{N.17} \end{equation}\] \(R_{act}^{RDOM}\) is the user specified refractory dissolved organic matter (i.e. carbon, nitrogen and phosphorus) activation 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. The parameters \(K_{miner-O_2}^{DOM}\), \(f_{an}\) and \(\theta_{miner}^{DOM}\) used in Equation (N.17) are the same as those used for the mineralisation calculations described in Section N.4 and specified via the associated labile organic matter mineralisation command. If this is the case and labile organic matter mineralisation is not required as a simulated process, then the command can still be issued but with the first argument, \(R_{miner}^{DOM}\), equal to zero.

N.5.1 Consumption

The activation rate from Equation (N.17) is multiplied by the ambient refractory dissolved carbon, nitrogen and phosphorus concentrations to compute their respective consumptive fluxes (losses) at each model timestep in each model cell via Equation (N.18).

\[\begin{equation} \left.\begin{aligned} \href{AppDiags.html#WQDiagActC}{F_{act\langle computed\rangle}^{RDOC}} =& R_{act\langle computed\rangle}^{RDOM} \times \left[ RDOC \right] \\ \\ \href{AppDiags.html#WQDiagActN}{F_{act\langle computed\rangle}^{RDON}} =& R_{act\langle computed\rangle}^{RDOM} \times \left[ RDON \right] \\ \\ \href{AppDiags.html#WQDiagActP}{F_{act\langle computed\rangle}^{RDOP}} =& R_{act\langle computed\rangle}^{RDOM} \times \left[ RDOP \right] \end{aligned}\right\} \tag{N.18} \end{equation}\]

N.5.2 Production

The consumptive flux from Equation (N.18) results in the labile dissolved organic carbon, nitrogen and phosphorus productive fluxes in Equation (N.19).

\[\begin{equation} \left.\begin{aligned} F_{act\langle computed\rangle}^{DOC} =& F_{act\langle computed\rangle}^{RDOC} \\ \\ F_{act\langle computed\rangle}^{DON} =& F_{act\langle computed\rangle}^{RDON} \\ \\ F_{act\langle computed\rangle}^{DOP} =& F_{act\langle computed\rangle}^{RDOP} \end{aligned}\right\} \tag{N.19} \end{equation}\]

N.6 Photolysis

The WQ Module conceptualises photolysis as the conversion of refractory dissolved organic carbon, nitrogen and phosphorus to their labile dissolved and inorganic equivalents, under the action of photosynthetically active (PAR), ultraviolet A (UVA) and ultraviolet B (UVB) radiation. These radiation bands are provided to the WQ Module from TUFLOW for each computational cell at each water quality timestep. The WQ Module computes total photolysis of refractory dissolved organic carbon \(F_{photo-tot}^{RDOC}\) as the sum of photolysis due to each of these three bands via Equation (N.20). \[\begin{equation} F_{photo-tot}^{RDOC} = F_{photo-PAR}^{RDOC} + F_{photo-UVA}^{RDOC} + F_{photo-UVB}^{RDOC} \tag{N.20} \end{equation}\] Each band’s photolysis is computed via Equation (N.21), with Radiation\(_{band}\) (where band is PAR, UVA or UVB) being previously converted from \(W/m^2\) (as provided by TUFLOW) to moles of photons. \[\begin{equation} F_{photo-band}^{RDOC} = \text{Radiation$_{band}$} \times \underbrace{c \times 10^{-d \times \lambda_{band}}}_{\text{Apparent quantum yield}} \times \underbrace{CDOM \times e^{S\times(x-\lambda_{band})}}_{\text{Absorption coefficient}} \tag{N.21} \end{equation}\] where \(c\) = 7.52, \(d\) = 0.0122, \(\lambda_{band}\) is each band’s characteristic wavelength, \(S\) = 0.0188 and \(x\) = 440.0 nm. \(CDOM\) is chromomorphic dissolved organic matter and is computed via Equation (N.22). \[\begin{equation} \href{AppDiags.html#WQDiagCDOM}{CDOM_{\langle computed \rangle}} = 0.35 \times e^{0.1922\times \left( \left[DOC\right] + \left[RDOC\right]\right) \times (12/1000)} \tag{N.22} \end{equation}\] \(\left[DOC\right]\) and \(\left[RDOC\right]\) and the ambient concentrations of labile and refractory dissolved organic carbon, respectively.

N.6.1 Consumption

Once total photolysis has been computed, the associated consumptive fluxes (losses) of refractory dissolved organic carbon, nitrogen and phosphorus are computed via Equation (N.23), using ambient refractory dissolved nitrogen and phosphorus concentrations to proportion the computed fluxes. \[\begin{equation} \left.\begin{aligned} \href{AppDiags.html#WQDiagPhoto}{F_{photo\langle computed\rangle}^{RDOC}} =& F_{photo-tot}^{RDOC} \\ \\ F_{photo\langle computed\rangle}^{RDON} =& F_{photo-tot}^{RDOC} \times \frac{\left[RDON\right]}{\left[RDOC\right]} \\ \\ F_{photo\langle computed\rangle}^{RDOP} =& F_{photo-tot}^{RDOC} \times \frac{\left[RDOP\right]}{\left[RDOC\right]} \end{aligned}\right\} \tag{N.23} \end{equation}\]

N.6.2 Production

The consumptive fluxes from Equation (N.23) result in the labile dissolved organic carbon, nitrogen and phosphorus productive fluxes in Equation (N.24). \[\begin{equation} \left.\begin{aligned} F_{photo\langle computed\rangle}^{DOC} =& F_{photo\langle computed\rangle}^{RDOC} \times f_{photo}^{RDOM} \\ \\ F_{photo\langle computed\rangle}^{DON} =& F_{photo\langle computed\rangle}^{RDON} \times f_{photo}^{RDOM} \\ \\ F_{photo\langle computed\rangle}^{DOP} =& F_{photo\langle computed\rangle}^{RDOP} \times f_{photo}^{RDOM} \end{aligned}\right\} \tag{N.24} \end{equation}\] \(f_{photo}^{RDOM}\) is the proportion of the total photolysed refractory dissolved organic matter that becomes the corresponding labile organics. The remainder of the photolysed refractory dissolved organic matter fluxes produce inorganic carbon and nutrients via Equation (N.25). \[\begin{equation} \left.\begin{aligned} F_{photo\langle computed\rangle}^{DIC} =& F_{photo\langle computed\rangle}^{RDOC} \times \left(1.0 - f_{photo}^{RDOM}\right) \\ \\ F_{photo\langle computed\rangle}^{NH_4} =& F_{photo\langle computed\rangle}^{RDON} \times \left(1.0 - f_{photo}^{RDOM}\right) \\ \\ F_{photo\langle computed\rangle}^{FRP} =& F_{photo\langle computed\rangle}^{RDOP} \times \left(1.0 - f_{photo}^{RDOM}\right) \end{aligned}\right\} \tag{N.25} \end{equation}\]

The WQ Module does not currently support simulation of dissolved inorganic carbon (DIC) so the corresponding carbonic productive flux in Equation (N.25) has no effect on inorganic water quality dynamics. Contact support@tuflow.com if the DIC model is required.

N.7 Self shading

Photosynthetically available radiation is provided to the WQ Module from TUFLOW for each computational cell at each water quality timestep. The WQ Module allows for modification of this TUFLOW field to incorporate the effect of light attenuation due to the presence of particulate and dissolved organic matter. This additional light extinction is computed dynamically at each water quality timestep, based on instantaneous organic matter concentrations in individual computational cells.

For labile organics, the associated additive specific light attenuation coefficient is computed as per Equation (N.26). \[\begin{equation} Ke_{\langle computed \rangle}^{OM} = Ke^{POM} \times \left[POC\right] + Ke^{DOM} \times \left[DOC\right] \tag{N.26} \end{equation}\] \(Ke^{POM}\) and \(Ke^{DOM}\) are the user specified (or default) specific shading coefficients for labile particulate and dissolved organic matter respectively, and \(\left[POC\right]\) and \(\left[DOC\right]\) are the ambient labile particulate and dissolved organic carbon concentrations (used as proxies for organic matter) in each cell. For each cell and at each timestep, this quantity \(Ke_{\langle computed \rangle}^{OM}\) is computed and returned to TUFLOW as a two- or three-dimensional field which TUFLOW then includes these in subsequent light distribution calculations.

For refractory organics (if computed), the associated additive specific light attenuation coefficient is computed as per Equation (N.27). \[\begin{equation} Ke_{\langle computed \rangle}^{ROM} = R_{CDOM}^{RDOM} \times CDOM + Ke^{RPOM} \times \left[RPOM\right] \tag{N.27} \end{equation}\] \(R_{CDOM}^{RDOM}\) is a user specified (or default) dimensionless multiplier applied to the CDOM computed in Equation (N.22), where the same CDOM is used in photolysis calculations. \(R_{CDOM}^{RDOM}\) is not a specific shading coefficient, but can be thought of as (light attenuation (/m) / CDOM (/m)), or the strength of CDOM in attenuating light. \(Ke^{RPOM}\) is the user specified (or default) specific shading coefficient for refractory particulate organic matter, and \(\left[RPOM\right]\) is the instantaneous refractory particulate organic matter concentration in each cell. For each cell and at each timestep, this quantity \(Ke_{\langle computed \rangle}^{ROM}\) is computed and returned to TUFLOW as a two- or three-dimensional field which TUFLOW then includes these in subsequent light distribution calculations.

N.8 Settling

Particulate organic matter is able to be settled within the WQ Module. Four settling models are available. These are able to be applied equally to both labile and refractory particulate organic matter to compute \(V_{settle}^{lorg}\) and \(V_{settle}^{rorg}\), respectively. The same settling model must be applied to both types of particulates, although the parameters ascribed to a model can be different for labile and refractory particulates. Once computed, the same settling rate is applied to each of labile particulate organic carbon, nitrogen and phosphorus.

N.8.1 None

In this model, particulate organic settling is set to zero and organic matter is simply advected by the hydrodynamic flow field.

N.8.2 Constant

In this model, \(V_{settle}^{lorg}\) and \(V_{settle}^{rorg}\) are set to constant values, and matter is settled at these velocities. These can be different velocities for labile and refractory particulate organics. A negative specification of this quantity corresponds to a downwards settling velocity.

N.8.3 Constant with density correction

In this model, \(V_{settle}^{lorg}\) and \(V_{settle}^{rorg}\) are set to constant values, and matter is settled at these velocities, but corrected for ambient water density effects, as per Equation (N.28).

\[\begin{equation} V_{sett\langle computed\rangle}^{org} = V_{settle}^{org} \times \frac{\mu_{20}\times\rho_w}{\mu\times\rho_{w20}} \tag{N.28} \end{equation}\]

\(V_{settle}^{org}\) is \(V_{settle}^{lorg}\) or \(V_{settle}^{rorg}\) at 20\(^o\)C, \(\mu\) and \(\rho_w\) are the ambient water dynamic viscosity (in Ns/m\(^2\)) and density (in kg/m\(^3\)), respectively, and \(\mu_{20}\) and \(\rho_{w20}\) are the dynamic viscosity and density of freshwater at 20\(^o\)C, respectively. A negative specification of \(V_{settle}^{org}\) corresponds to a downwards settling velocity.

N.8.4 Stokes

In this model, particulate organic settling is computed using the Stokes equation and particle diameter and density, as per Equations (N.29) and (N.30).

\[\begin{equation} V_{sett\langle computed\rangle}^{lorg} = -g \times d_{lorg}^2 \times \frac{\left(\rho_{lorg}-\rho_w\right)}{18\mu} \tag{N.29} \end{equation}\]

\[\begin{equation} V_{sett\langle computed\rangle}^{rorg} = -g \times d_{rorg}^2 \times \frac{\left(\rho_{rorg}-\rho_w\right)}{18\mu} \tag{N.30} \end{equation}\] \(g\) is acceleration due to gravity, \(d_{lorg}\) and \(d_{rorg}\) are conceptualised diameters of labile and refractory particulate organic matter respectively, \(\rho_{lorg}\) and \(\rho_{rorg}\) are labile and refractory particulate organic matter densities, respectively, and \(\rho_w\) and \(\mu\) are the ambient water density and dynamic viscosity, respectively.

Once the settling velocities for labile and refractory particulate organic matter have been computed, the relevant fluxes are calculated as follows.

\[\begin{equation} \left.\begin{aligned} \href{AppDiags.html#WQDiagPOCSedmtn}{F_{sedmtn\langle computed\rangle}^{POC}} =& \frac{\href{AppDiags.html#WQDiagPOMVVel}{V_{settle\langle computed \rangle}^{lorg}}}{dz} \times \left[ POC \right] \\ \\ \href{AppDiags.html#WQDiagPONSedmtn}{F_{sedmtn\langle computed\rangle}^{PON}} =& \frac{\href{AppDiags.html#WQDiagPOMVVel}{V_{settle\langle computed \rangle}^{lorg}}}{dz} \times \left[ PON \right] \\ \\ \href{AppDiags.html#WQDiagPOPSedmtn}{F_{sedmtn\langle computed\rangle}^{POP}} =& \frac{\href{AppDiags.html#WQDiagPOMVVel}{V_{settle\langle computed \rangle}^{lorg}}}{dz} \times \left[ POP \right] \end{aligned}\right\} \tag{N.31} \end{equation}\]

\[\begin{equation} \href{AppDiags.html#WQDiagRPOMSedmtn}{F_{sedmtn\langle computed\rangle}^{RPOM}} = \frac{\href{AppDiags.html#WQDiagRPOMVVel}{V_{settle\langle computed \rangle}^{rorg}}}{dz} \times \left[ RPOM \right] \tag{N.32} \end{equation}\] \(dz\) is the relevant cell thickness, and divides the flux to produce a per volume result for consistency with other corresponding diagnostics.

The limitations of this approach to modelling particulate organic matter settling are recognised. Future releases of the WQ Module will offer direct linkages between the TUFLOW FV ST Module and WQ Module, and treat particulate organics as sediment fractions that are transported using the advanced techniques and models offered by the ST Module.