F.3 Denitrification

Denitrification is the pelagic biological reduction of nitrate to free nitrogen gas, \(N_2\). This typically occurs as a result of microbial oxygen stripping from nitrate in low dissolved oxygen environments. It occurs through a series of intermediate stages, but is typically represented as a single-step process with a governing denitrification rate. This rate is computed within the WQ Module via either Equation (F.5) or (F.6). These are identical other than their treatment of the influence of dissolved oxygen on denitrification, which is either Michaelis-Menten or exponential, respectively. Unlike nitrification, denitrification includes the influence of nitrate concentration in both rate calculations, again in a Michaelis-Menten form.

\[\begin{equation} R_{denit\langle computed\rangle}^{NO_3} = R_{denit}^{NO_3} \hphantom{\text{abc}} \times \hphantom{\text{abc}} \frac{K_{denit-O_2-MM}^{NO_3}}{K_{denit-O_2-MM}^{NO_3} + \left[DO\right]} \times \left[\theta_{denit}^{NO_3}\right]^{\left(T-20\right)} \times \frac{\left[NO_3\right]}{K_{denit-NO_3}^{NO_3} + \left[NO_3\right]} \tag{F.5} \end{equation}\]

\[\begin{equation} R_{denit\langle computed\rangle}^{NO_3} = R_{denit}^{NO_3} \hphantom{\text{abc}} \times \hphantom{\text{abc}} \underbrace{\vphantom{\frac{\left[NO_3\right]}{K_{denit-NO_3}^{NO_3} + \left[NO_3\right]}}{\rm e}^{\left[\frac{-\left[DO\right]}{K_{denit-O_2-exp}^{NO_3}}\right]}}_{\text{Influence of oxygen}} \times \hphantom{\text{abcd}} \underbrace{\vphantom{\frac{\left[NO_3\right]}{K_{denit-NO_3}^{NO_3} + \left[NO_3\right]}}\left[\theta_{denit}^{NO_3}\right]^{\left(T-20\right)}}_{\text{Influence of temperature}} \times \underbrace{\frac{\left[NO_3\right]}{K_{denit-NO_3}^{NO_3} + \left[NO_3\right]}}_{\text{Influence of nitrate}} \tag{F.6} \end{equation}\]

\(R_{denit}^{NO_3}\) is the user specified nitrate denitrification rate at 20\(^o\)C and without the influence of dissolved oxygen, and \(\left[DO\right]\) and \(\left[NO_3\right]\) are the ambient dissolved oxygen and nitrate concentrations respectively. If the Michaelis-Menten oxygen model is used then \(K_{denit-O2-MM}^{NO_3}\) is the half saturation concentration of oxygen for denitrification. If the exponential model is used then \(K_{denit-O2-exp}^{NO_3}\) is the dissolved oxygen concentration that normalises (i.e. non-dimensionalises) the ambient oxygen concentration used in Equation (F.6). Equation (F.5) is the default. Finally, \(\theta_{denit}^{NO_3}\) is the temperature coefficient for denitrification of nitrate, \(T\) is ambient water temperature, and \(K_{denit-NO_3}^{NO_3}\) is the Michaelis-Menten half saturation nitrate concentration that influences denitrification in both Equations (F.5) and (F.6). \(K_{denit-NO_3}^{NO_3}\) is not user definable, but hardwired to a value of 0.07 mg/L of nitrate (5.0 mmol/m\(^3\)).

The computed denitrification rate from Equation (F.5) or (F.6) is then multiplied by ambient nitrate concentration to compute the flux of nitrate to free nitrogen gas at each model timestep in each model cell via Equation (F.7).

\[\begin{equation} \href{AppDiags.html#WQDiagDenitrif}{F_{denit\langle computed\rangle}^{NO_3}} = R_{denit\langle computed\rangle}^{NO_3} \times \left[ NO_3 \right] \tag{F.7} \end{equation}\]

Unlike nitrification, denitrification does not produce or consume dissolved oxygen. It does, however, consume nitrate and therefore presents a feedback loop in Equations (F.5) through (F.7).

The demonstration model was executed over two suites of identical simulations that varied temperature from one simulation to the next, with the first suite using Equation (F.5) and the second suite using Equation (F.6). Only denitrification was turned on, and constant values for \(R_{denit}^{NO_3}\) (1.5/day - a deliberately very large value was chosen to demonstrate trends), \(K_{denit-O_2}^{NO_3}\) (4 mg/L) and \(K_{denit-NO_3}^{NO_3}\) (15.5 mg/L) were set. Temperature coefficients were set to 1.05. The predicted temporal evolution of water column nitrate concentrations in these simulation pairs are provided in Figure F.4.

Figure F.4: Move the slider to see the effect of changing temperature on the concentrations of nitrate, where two different denitrification models are used

The figure demonstrates the expected behaviour, where nitrate is consumed in a non-linear manner. The different models produce different drawdown rates, also as expected. In this example, these differences are substantial.

The same two suites of demonstration models were also used to illustrate the influence of varying \(K_{denit-O_2}^{NO_3}\) (instead of temperature) on denitrification. All set ups from the models used above were retained, other than setting ambient water temperature to constant at 20 \(^o\)C, and allowing \(K_{denit-O_2}^{NO_3}\) to vary. The predicted temporal evolution of water column nitrate concentrations in these demonstration model simulation pairs are provided in Figure F.5.

Figure F.5: Move the slider to see the effect of changing \(K_{denit-O_2}^{NO_3}\) on the concentrations of nitrate, where two different denitrification models are used

Substantial differences in the prediction of nitrate concentrations is again observed, especially at lower half saturation concentrations.