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 nitrite (NO2−) in the stream will be increased by the conversion of NH4+ to NO2− and decreased by the conversion of NO2− to NO3−. The conversion of NO2− to NO3− occurs more rapidly than the conversion of NH4+ to NO2−, so the amount of nitrite present in the stream is usually very small. The change in nitrite for a given day is:
ΔNO2str=(βN,1∗NH4str−βN,2∗NO2str)∗TT 7:3.2.8
where ΔNO2str is the change in nitrite concentration (mg N/L), βN,1 is the rate constant for biological oxidation of ammonia nitrogen (day−1 or hr−1), NH4str is the ammonium concentration at the beginning of the day (mg N/L), βN,2 is the rate constant for biological oxidation of nitrite to nitrate (day−1 or hr−1), NO2str is the nitrite concentration at the beginning of the day (mg N/L), and 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:
7:3.2.9
where is the rate constant for biological oxidation of nitrite to nitrate (day or hr), is the rate constant for biological oxidation of nitrite to nitrate at 20C (day or hr), is the dissolved oxygen concentration in the stream (mg O/L), and is the average water temperature for the day or hour (C). The second term on the right side of equation 7:3.2.9, , is a nitrification inhibition correction factor. This factor inhibits nitrification at low dissolved oxygen concentrations.
The amount of nitrate () in the stream may be increased by the oxidation of . The nitrate concentration in the stream may be decreased by the uptake of by algae. The change in nitrate for a given day is:
7:3.2.10
where is the change in nitrate concentration (mg N/L), is the rate constant for biological oxidation of nitrite to nitrate (day or hr), is the nitrite concentration at the beginning of the day (mg N/L), is the fraction of algal nitrogen uptake from ammonium pool, is the fraction of algal biomass that is nitrogen (mg N/mg alg biomass), is the local growth rate of algae (day or hr), is the algal biomass concentration at the beginning of the day (mg alg/L), and 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.
The amount of ammonium (NH) 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 to NO or the uptake of NH by algae. The change in ammonium for a given day is:
7:3.2.4
where is the change in ammonium concentration (mg N/L), is the rate constant for hydrolysis of organic nitrogen to ammonia nitrogen (day or hr), is the organic nitrogen concentration at the beginning of the day (mg N/L), is the rate constant for biological oxidation of ammonia nitrogen (day
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 or the settling of organic nitrogen with sediment. The change in organic nitrogen for a given day is:
7:3.2.1
where is the change in organic nitrogen concentration (mg N/L), is the fraction of algal biomass that is nitrogen (mg N/mg alg biomass), is the local respiration or death rate of algae (day or hr), is the algal biomass concentration at the beginning of the day (mg alg/L), is the rate constant for hydrolysis of organic nitrogen to ammonia nitrogen (day or hr), is the organic nitrogen concentration at the beginning of the day (mg N/L), is the rate coefficient for organic nitrogen settling (day or hr), and
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:
βN,1=βN,1,20∗(1−exp[−0.6∗Oxstr])∗1.083(Twater−20) 7:3.2.5
where βN,1 is the rate constant for biological oxidation of ammonia nitrogen (day−1 or hr−1), βN,1,20 is the rate constant for biological oxidation of ammonia nitrogen at 20°C (day−1 or hr−1), Oxstr is the dissolved oxygen concentration in the stream (mg O2/L), and Twater is the average water temperature for the day or hour (°C). The second term on the right side of equation 7:3.2.5,(1−exp[−0.6∗Oxstr]), 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°C. The benthos source rate for ammonium nitrogen is adjusted to the local water temperature using the relationship:
σ3=σ3,20∗1.074(Twater−20) 7:3.2.6
where σ3 is the benthos (sediment) source rate for ammonium (mg N/m2-day or mg N/m22-hr), σ3,20 is the benthos (sediment) source rate for ammonium nitrogen at 20°C (mg N/m2-day or mg N/m2-hr), and Twater is the average water temperature for the day or hour (°C).
The fraction of algal nitrogen uptake from ammonium pool is calculated:
frNH4=(fNH4∗NH4str+(1−fNH4)∗NO3str)fNH4∗NH4str 7:3.2.7
where frNH4 is the fraction of algal nitrogen uptake from ammonium pool, fNH4 is the preference factor for ammonia nitrogen, NH4str is the ammonium concentration in the stream (mg N/L), and NO3str is the nitrate concentration in the stream (mg N/L).
The user defines the local rate constant for hydrolysis of organic nitrogen to NH4+ at 20°C. The organic nitrogen hydrolysis rate is adjusted to the local water temperature using the relationship:
βN,3=βN,3,20∗1.047(Twater−20) 7:3.2.2
where βN,3 is the local rate constant for hydrolysis of organic nitrogen to NH4+ (day−1 or hr−1), βN,3,20 is the local rate constant for hydrolysis of organic nitrogen to NH4+ at 20°C (day−1 or hr−1), and Twater is the average water temperature for the day or hour (°C).
The user defines the rate coefficient for organic nitrogen settling at 20°C. The organic nitrogen settling rate is adjusted to the local water temperature using the relationship:
σ4=σ4,20∗1.024(Twater−20) 7:3.2.3
where σ4 is the local settling rate for organic nitrogen (day−1 or hr−1), σ4,20 is the local settling rate for organic nitrogen at 20°C (day−1 or hr−1), and Twater is the average water temperature for the day or hour (°C).
Table 7:3-2: SWAT+ input variables used in in-stream nitrogen calculations.
AI1
: Fraction of algal biomass that is nitrogen (mg N/mg alg biomass)
.wwq
RHOQ
: Local algal respiration rate at 20C (day)
.wwq
BC3
: Local rate constant for hydrolysis of organic nitrogen to NH at 20C (day or hr)
.swq
RS4
σ4,20: Local settling rate for organic nitrogen at 20°C (day−1)
.swq
BC1
βN,1,20: Rate constant for biological oxidation of ammonia nitrogen at 20°C (day−1)
.swq
RS3
σ3,20: Benthos (sediment) source rate for ammonium nitrogen at 20°C (mg N/m2-day or mg N/m2-hr)
.swq
P_N
fNH4: Preference factor for ammonia nitrogen
.wwq
BC2
βN,2,20: Rate constant for biological oxidation of nitrite to nitrate at 20°C (day−1 or hr−1)
.swq