The amount of organic nitrogen in the stream may be increased by the conversion of algal biomass nitrogen to organic nitrogen. Organic nitrogen concentration in the stream may be decreased by the conversion of organic nitrogen to NH$^+_4$ or the settling of organic nitrogen with sediment. The change in organic nitrogen for a given day is:

$\Delta orgN_{str}=(\alpha_1 * \rho_a*algae-\beta_{N,3}*orgN_{str}-\sigma_4*orgN_{str})*TT$ 7:3.2.1

where $\Delta_{orgN_{str}}$ is the change in organic nitrogen concentration (mg N/L), $\alpha_1$ is the fraction of algal biomass that is nitrogen (mg N/mg alg biomass), $\rho_a$ is the local respiration or death rate of algae (day$^{-1}$ or hr$^{-1}$), $algae$ is the algal biomass concentration at the beginning of the day (mg alg/L), $\beta_{N,3}$ is the rate constant for hydrolysis of organic nitrogen to ammonia nitrogen (day$^{-1}$ or hr$^{-1}$), $orgN_{str}$ is the organic nitrogen concentration at the beginning of the day (mg N/L), $\sigma_4$ is the rate coefficient for organic nitrogen settling (day$^{-1}$ or hr$^{-1}$), and $TT$ is the flow travel time in the reach segment (day or hr). The fraction of algal biomass that is nitrogen is user-defined. Equation 7:3.1.17 describes the calculation of the local respiration rate of algae. The calculation of travel time is reviewed in Chapter 7:1.

The user defines the local rate constant for hydrolysis of organic nitrogen to NH$^+_4$ at 20$\degree$C. The organic nitrogen hydrolysis rate is adjusted to the local water temperature using the relationship:

$\beta_{N,3}=\beta_{N,3,20}*1.047^{(T_{water}-20)}$ 7:3.2.2

where $\beta_{N,3}$ is the local rate constant for hydrolysis of organic nitrogen to NH$^+_4$ (day$^{-1}$ or hr$^{-1}$), $\beta_{N,3,20}$ is the local rate constant for hydrolysis of organic nitrogen to NH$^+_4$ at 20$\degree$C (day$^{-1}$ or hr$^{-1}$), and $T_{water}$ is the average water temperature for the day or hour ($\degree$C).

The user defines the rate coefficient for organic nitrogen settling at 20$\degree$C. The organic nitrogen settling rate is adjusted to the local water temperature using the relationship:

$\sigma_4=\sigma_{4,20}*1.024^{(T_{water}-20)}$ 7:3.2.3

where $\sigma_4$ is the local settling rate for organic nitrogen (day$^{-1}$ or hr$^{-1}$), $\sigma_{4,20}$ is the local settling rate for organic nitrogen at 20$\degree$C (day$^{-1}$ or hr$^{-1}$), and $T_{water}$ is the average water temperature for the day or hour ($\degree$C).

The amount of ammonium (NH$^+_4$) in the stream may be increased by the mineralization of organic nitrogen and diffusion of ammonium from the streambed sediments. The ammonium concentration in the stream may be decreased by the conversion of NH$^+_4$ to NO$^-_2$ or the uptake of NH$^+_4$ by algae. The change in ammonium for a given day is:

$\Delta NH4_{str}=(\beta_{N,3}*orgN_{str}-\beta_{N,1}*NH4_{str}+\frac{\sigma_3}{(1000*depth)}-fr_{NH4}*\alpha_1*\mu_a*algae)*TT$

7:3.2.4

where $\Delta NH4_{str}$ is the change in ammonium concentration (mg N/L), $\beta_{N,3}$ is the rate constant for hydrolysis of organic nitrogen to ammonia nitrogen (day$^{-1}$ or hr$^{-1}$), $orgN_{str}$ is the organic nitrogen concentration at the beginning of the day (mg N/L), $\beta_{N,1}$ is the rate constant for biological oxidation of ammonia nitrogen (day$^{-1}$ or hr$^{-1}$), $NH4_{str}$ is the ammonium concentration at the beginning of the day (mg N/L), $\sigma_3$ is the benthos (sediment) source rate for ammonium (mg N/m$^2$-day or mg N/m$^2$-hr), $depth$ is the depth of water in the channel (m), $fr_{NH4}$ is the fraction of algal nitrogen uptake from ammonium pool, $\alpha_1$ is the fraction of algal biomass that is nitrogen (mg N/mg alg biomass), $\mu _a$ is the local growth rate of algae (day$^{-1}$ or hr$^{-1}$), $algae$ is the algal biomass concentration at the beginning of the day (mg alg/L), and $TT$ is the flow travel time in the reach segment (day or hr). The local rate constant for hydrolysis of organic nitrogen to NH$^+_4$ is calculated with equation 7:3.2.2. Section 7:3.1.2.1 describes the calculation of the local growth rate of algae. The calculation of depth and travel time is reviewed in Chapter 7:1.

The rate constant for biological oxidation of ammonia nitrogen will vary as a function of in-stream oxygen concentration and temperature. The rate constant is calculated:

$\beta_{N,1}=\beta_{N,1,20}*(1-exp[-0.6*Ox_{str}])*1.083^{(T_{water}-20)}$ 7:3.2.5

where $\beta_{N,1}$ is the rate constant for biological oxidation of ammonia nitrogen (day$^{-1}$ or hr$^{-1}$), $\beta_{N,1,20}$ is the rate constant for biological oxidation of ammonia nitrogen at 20$\degree$C (day$^{-1}$ or hr$^{-1}$), $Ox_{str}$ is the dissolved oxygen concentration in the stream (mg O$_2$/L), and $T_{water}$ is the average water temperature for the day or hour ($\degree$C). The second term on the right side of equation 7:3.2.5,$(1-exp[-0.6*Ox_{str}])$, is a nitrification inhibition correction factor. This factor inhibits nitrification at low dissolved oxygen concentrations.

The user defines the benthos source rate for ammonium at 20$\degree$C. The benthos source rate for ammonium nitrogen is adjusted to the local water temperature using the relationship:

$\sigma_3=\sigma_{3,20}*1.074^{(T_{water}-20)}$ 7:3.2.6

where $\sigma_3$ is the benthos (sediment) source rate for ammonium (mg N/m$^2$-day or mg N/m$^2$2-hr), $\sigma_{3,20}$ is the benthos (sediment) source rate for ammonium nitrogen at 20$\degree$C (mg N/m$^2$-day or mg N/m$^2$-hr), and $T_{water}$ is the average water temperature for the day or hour ($\degree$C).

The fraction of algal nitrogen uptake from ammonium pool is calculated:

$fr_{NH4}=\frac{f_{NH4}*NH4_{str}}{(f_{NH4}*NH4_{str}+(1-f_{NH4})*NO3_{str})}$ 7:3.2.7

where $fr_{NH4}$ is the fraction of algal nitrogen uptake from ammonium pool, $f_{NH4}$ is the preference factor for ammonia nitrogen, $NH4_{str}$ is the ammonium concentration in the stream (mg N/L), and $NO3_{str}$ is the nitrate concentration in the stream (mg N/L).

The amount of nitrite ($NO_2^-$) in the stream will be increased by the conversion of $NH_4^+$ to $NO_2^-$ and decreased by the conversion of $NO_2^-$ to $NO_3^-$. The conversion of $NO_2^-$ to $NO_3^-$ occurs more rapidly than the conversion of $NH_4^+$ to $NO_2^-$, so the amount of nitrite present in the stream is usually very small. The change in nitrite for a given day is:

$\Delta NO2_{str}=(\beta_{N,1}*NH4_{str}-\beta_{N,2}*NO2_{str})*TT$ 7:3.2.8

where $\Delta NO2_{str}$ is the change in nitrite concentration (mg N/L), $\beta_{N,1}$ is the rate constant for biological oxidation of ammonia nitrogen (day$^{-1}$ or hr$^{-1}$), $NH4_{str}$ is the ammonium concentration at the beginning of the day (mg N/L), $\beta_{N,2}$ is the rate constant for biological oxidation of nitrite to nitrate (day$^{-1}$ or hr$^{-1}$), $NO2_{str}$ is the nitrite concentration at the beginning of the day (mg N/L), and $TT$ is the flow travel time in the reach segment (day or hr). The local rate constant for biological oxidation of ammonia nitrogen is calculated with equation 7:3.2.5. The calculation of travel time is reviewed in Chapter 7:1.

The rate constant for biological oxidation of nitrite to nitrate will vary as a function of in-stream oxygen concentration and temperature. The rate constant is calculated:

$\beta_{N,2}=\beta_{N,2,20}*(1-exp[-0.6*Ox_{str}])*1.047^{(T_{water}-20)}$ 7:3.2.9

where $\beta_{N,2}$ is the rate constant for biological oxidation of nitrite to nitrate (day$^{-1}$ or hr$^{-1}$), $\beta_{N,2,20}$ is the rate constant for biological oxidation of nitrite to nitrate at 20$\degree$C (day$^{-1}$ or hr$^{-1}$),$Ox_{str}$ is the dissolved oxygen concentration in the stream (mg O$_2$/L), and $T_{water}$ is the average water temperature for the day or hour ($\degree$C). The second term on the right side of equation 7:3.2.9, $(1-exp[-0.6*Ox_{str}])$, is a nitrification inhibition correction factor. This factor inhibits nitrification at low dissolved oxygen concentrations.

In aerobic water, there is a stepwise transformation from organic nitrogen to ammonia, to nitrite, and finally to nitrate. Organic nitrogen may also be removed from the stream by settling. This section summarizes the equations used to simulate the nitrogen cycle in the stream.

The amount of nitrate ($NO_3^-$) in the stream may be increased by the oxidation of $NO_2^-$. The nitrate concentration in the stream may be decreased by the uptake of $NO_3^-$ by algae. The change in nitrate for a given day is:

$\Delta NO3_{str}=(\beta_{N,2}*NO2_{str}-(1-fr_{NH4})*\alpha_1*\mu_a*algae)*TT$ 7:3.2.10

where $\Delta NO3_{str}$ is the change in nitrate concentration (mg N/L), $\beta_{N,2}$ is the rate constant for biological oxidation of nitrite to nitrate (day$^{-1}$ or hr$^{-1}$), $NO2_{str}$ is the nitrite concentration at the beginning of the day (mg N/L), $fr_{NH4}$ is the fraction of algal nitrogen uptake from ammonium pool, $\alpha_1$ is the fraction of algal biomass that is nitrogen (mg N/mg alg biomass), $\mu _a$ is the local growth rate of algae (day$^{-1}$ or hr$^{-1}$), $algae$ is the algal biomass concentration at the beginning of the day (mg alg/L), and $TT$ is the flow travel time in the reach segment (day or hr). The local rate constant for biological oxidation of nitrite to nitrate is calculated with equation 7:3.2.9 while the fraction of algal nitrogen uptake from ammonium pool is calculated with equation 7:3.2.7. Section 7:3.1.2.1 describes the calculation of the local growth rate of algae. The calculation of travel time is reviewed in Chapter 7:1.

Table 7:3-2: SWAT+ input variables used in in-stream nitrogen calculations.