The transport of nutrients from land areas into streams and water bodies is a normal result of soil weathering and erosion processes. However, excessive loading of nutrients into streams and water bodies will accelerate eutrophication and render the water unfit for human consumption. This chapter reviews the algorithms governing movement of mineral and organic forms of nitrogen and phosphorus from land areas to the stream network.

In large subbasins with a time of concentration greater than 1 day, only a portion of the surface runoff and lateral flow will reach the main channel on the day it is generated. SWAT+ incorporates a storage feature to lag a portion of the surface runoff and lateral flow release to the main channel. Nutrients in the surface runoff and lateral flow are lagged as well.

Once the nutrient load in surface runoff and lateral flow is determined, the amount of nutrients released to the main channel is calculated:

$NO3_{surf}=(NO3'_{surf}+NO3_{surstor,i-1})*(1-exp[\frac{-surlag}{t_{conc}}])$ 4:2.5.1

$NO3_{lat}=(NO3'_{lat}+NO3_{latstor,i-1})*(1-exp[\frac{-1}{TT_{lat}}])$ 4:2.5.2

$orgN_{surf}=(orgN'_{surf}+orgN_{stor,i-1})*(1-exp[\frac{-surlag}{t_{conc}}])$ 4:2.5.3

$P_{surf}=(P'_{surf}+P_{stor,i-1})*(1-exp[\frac{-surlag}{t_{conc}}])$ 4:2.5.4

$sedP_{surf}=(sedP'_{surf}+sedP_{stor,i-1})*(1-exp[\frac{-surlag}{t_{conc}}])$ 4:2.5.5

where $NO3_{surf}$ is the amount of nitrate discharged to the main channel in surface runoff on a given day (kg N/ha),$NO3'_{surf}$ is the amount of surface runoff nitrate generated in the HRU on a given day (kg N/ha), $NO3_{surstor,i-1}$ is the surface runoff nitrate stored or lagged from the previous day (kg N/ha), $NO3_{lat}$ is the amount of nitrate discharged to the main channel in lateral flow on a given day (kg N/ha), $NO3'_{lat}$ is the amount of lateral flow nitrate generated in the HRU on a given day (kg N/ha), $NO3_{latstor,i-1}$ is the lateral flow nitrate stored or lagged from the previous day (kg N/ha), $orgN_{surf}$ is the amount of organic N discharged to the main channel in surface runoff on a given day (kg N/ha),$orgN'_{surf}$ is the organic N loading generated in the HRU on a given day (kg N/ha), $orgN_{stor,i-1}$ is the organic N stored or lagged from the previous day (kg N/ha), $P_{surf}$ is the amount of solution P discharged to the main channel in surface runoff on a given day (kg P/ha), $P'_{surf}$ is the amount of solution P loading generated in the HRU on a given day (kg P/ha), $P_{stor,i-1}$ is the solution P loading stored or lagged from the previous day (kg P/ha), $sedP_{surf}$ is the amount of sediment-attached P discharged to the main channel in surface runoff on a given day (kg P/ha), $sedP'_{surf}$ is the amount of sediment-attached P loading generated in the HRU on a given day (kg P/ha), $sedP_{stor,i-1}$ is the sediment-attached P stored or lagged from the previous day (kg P/ha), $surlag$ is the surface runoff lag coefficient, $t_{conc}$ is the time of concentration for the HRU (hrs) and $TT_{lag}$ is the lateral flow travel time (days).

Table 4:2-5: SWAT+ input variables that pertain to nutrient lag calculations.

Organic N attached to soil particles may be transported by surface runoff to the main channel. This form of nitrogen is associated with the sediment loading from the HRU and changes in sediment loading will be reflected in the organic nitrogen loading. The amount of organic nitrogen transported with sediment to the stream is calculated with a loading function developed by McElroy et al. (1976) and modified by Williams and Hann (1978).

$orgN_{surf}=0.001*conc_{orgN}*\frac{sed}{area_{hru}}*\varepsilon_{N:sed}$ 4:2.2.1

where $orgN_{surf}$ is the amount of organic nitrogen transported to the main channel in surface runoff (kg N/ha), $conc_{orgN}$ is the concentration of organic nitrogen in the top 10 mm (g N/ metric ton soil), $sed$ is the sediment yield on a given day (metric tons), $area_{hru}$ is the HRU area (ha), and $\varepsilon_{N:sed}$ is the nitrogen enrichment ratio.

The concentration of organic nitrogen in the soil surface layer, $conc_{orgN}$, is calculated:

$conc_{orgN}=100*\frac{(orgN_{frsh,surf}+orgN_{sta,surf}+orgN_{act,surf})}{\rho_b*depth_{surf}}$ 4:2.2.2

where $orgN_{frsh,surf}$ is nitrogen in the fresh organic pool in the top 10mm (kg N/ha), $orgN_{sta,surf}$ is nitrogen in the stable organic pool (kg N/ha), $orgN_{act,surf}$ is nitrogen in the active organic pool in the top 10 mm (kg N/ha), $\rho_b$ is the bulk density of the first soil layer (Mg/m$^3$), and $depth_{surf}$ is the depth of the soil surface layer (10 mm).

Most soil minerals are negatively charged at normal pH and the net interaction with anions such as nitrate is a repulsion from particle surfaces. This repulsion is termed negative adsorption or anion exclusion.

Anions are excluded from the area immediately adjacent to mineral surfaces due to preferential attraction of cations to these sites. This process has a direct impact on the transport of anions through the soil for it effectively excludes anions from the slowest moving portion of the soil water volume found closest to the charged particle surfaces (Jury et al, 1991). In effect, the net pathway of the anion through the soil is shorter than it would be if all the soil water had to be used (Thomas and McMahon, 1972).

Nitrate may be transported with surface runoff, lateral flow or percolation. To calculate the amount of nitrate moved with the water, the concentration of nitrate in the mobile water is calculated. This concentration is then multiplied by the volume of water moving in each pathway to obtain the mass of nitrate lost from the soil layer.

The concentration of nitrate in the mobile water fraction is calculated:

$conc_{NO3,mobile}=\frac{NO3_{ly}*(1-exp[\frac{-w_{mobile}}{(1-\theta_e)*SAT_{ly}}])}{w_{mobile}}$ 4:2.1.2

where $conc_{NO3,mobile}$ is the concentration of nitrate in the mobile water for a given layer (kg N/mm H$_2$O), $NO3_{ly}$ is the amount of nitrate in the layer (kg N/ha), $w_{mobile}$ is the amount of mobile water in the layer (mm H$_2$O), $\theta_e$ is the fraction of porosity from which anions are excluded, and $SAT_{ly}$ is the saturated water content of the soil layer (mm H$_2$O). The amount of mobile water in the layer is the amount of water lost by surface runoff, lateral flow or percolation:

$w_{mobile}=Q_{surf}+Q_{lat,ly}+w_{perc,ly}$ for top 10 mm 4:2.1.3

$w_{mobile}=Q_{lat,ly}+w_{perc,ly}$ for lower soil layers 4:2.1.4

where $w_{mobile}$ is the amount of mobile water in the layer (mm H$_2$O), $Q_{surf}$ is the surface runoff generated on a given day (mm H$_2$O), $Q_{lat,ly}$ is the water discharged from the layer by lateral flow (mm H$_2$O), and $w_{perc,ly}$ is the amount of water percolating to the underlying soil layer on a given day (mm H$_2$O). Surface runoff is allowed to interact with and transport nutrients from the top 10 mm of soil.

Nitrate removed in surface runoff is calculated:

$NO3_{surf}=\beta_{NO3}*conc_{NO3,mobile}*Q_{surf}$ 4:2.1.5

where $NO3_{surf}$ is the nitrate removed in surface runoff (kg N/ha), $\beta_{NO3}$ is the nitrate percolation coefficient, $conc_{NO3,mobile}$ is the concentration of nitrate in the mobile water for the top 10 mm of soil (kg N/mm H$_2$O), and $Q_{surf}$ is the surface runoff generated on a given day (mm H$_2$O). The nitrate percolation coefficient allows the user to set the concentration of nitrate in surface runoff to a fraction of the concentration in percolate.

Nitrate removed in lateral flow is calculated:

$NO3_{lat,ly}=\beta_{NO3}*conc_{NO3,mobile}*Q_{lat,ly}$ for top 10 mm 4:2.1.6

$NO3_{lat,ly}=conc_{NO3,mobile}*Q_{lat,ly}$ for lower layers 4:2.1.7

where $NO3_{lat,ly}$ is the nitrate removed in lateral flow from a layer (kg N/ha), $\beta_{NO3}$ is the nitrate percolation coefficient, $conc_{NO3,mobile}$ is the concentration of nitrate in the mobile water for the layer (kg N/mm H$_2$O), and $Q_{lat,ly}$ is the water discharged from the layer by lateral flow (mm H$_2$O).

Nitrate moved to the underlying layer by percolation is calculated:

$NO3_{perc,ly}=conc_{NO3,mobile}*w_{perc,ly}$ 4:2.1.8

where $NO3_{perc,ly}$ is the nitrate moved to the underlying layer by percolation (kg N/ha), $conc_{NO3,mobile}$ is the concentration of nitrate in the mobile water for the layer (kg N/mm H$_2$O), and $w_{perc,ly}$ is the amount of water percolating to the underlying soil layer on a given day (mm H$_2$O).

Table 4:2-1: SWAT+ input variables that pertain to nitrate transport.

The enrichment ratio is defined as the ratio of the concentration of phosphorus transported with the sediment to the concentration of phosphorus in the soil surface layer. SWAT+ will calculate an enrichment ratio for each storm event, or allow the user to define a particular enrichment ratio for phosphorus attached to sediment that is used for all storms during the simulation. To calculate the enrichment ratio, SWAT+ uses a relationship described by Menzel (1980) in which the enrichment ratio is logarithmically related to sediment concentration. The equation used to calculate the phosphorus enrichment ratio, $\varepsilon_{P:sed}$, for each storm event is:

$\varepsilon_{P:sed}=0.78*(conc_{sed,surq})^{-0.2468}$ 4:2.4.3

where $conc_{sed,surq}$ is the concentration of sediment in surface runoff (Mg $sed$/m$^3$ H$_2$O). The concentration of sediment in surface runoff is calculated:

$conc_{sed,surq}=\frac{sed}{10*area_{hru}*Q_{surf}}$ 4:2.4.4

where $sed$ is the sediment yield on a given day (metric tons), $area_{hru}$ is the HRU area (ha), and $Q_{surf}$ is the amount of surface runoff on a given day (mm H$_2$O).

Table 4:2-4: SWAT+ input variables that pertain to loading of P attached to sediment.

The primary mechanism of phosphorus movement in the soil is by diffusion. Diffusion is the migration of ions over small distances (1-2 mm) in the soil solution in response to a concentration gradient. Due to the low mobility of solution phosphorus, surface runoff will only partially interact with the solution P stored in the top 10 mm of soil. The amount of solution P transported in surface runoff is:

$P_{surf}=\frac{P_{solution,surf}*Q_{surf}}{\rho_b*depth_{surf}*k_{d,surf}}$ 4:2.3.1

where $P_{surf}$ is the amount of soluble phosphorus lost in surface runoff (kg P/ha), $P_{solution,surf}$ is the amount of phosphorus in solution in the top 10 mm (kg P/ha), $Q_{surf}$ is the amount of surface runoff on a given day (mm H$_2$O), $\rho_b$ is the bulk density of the top 10 mm (Mg/m$^3$) (assumed to be equivalent to bulk density of first soil layer), $depth_{surf}$ is the depth of the “surface” layer (10 mm), and $k_{d,surf}$ is the phosphorus soil partitioning coefficient (m$^3$/Mg). The phosphorus soil partitioning coefficient is the ratio of the soluble phosphorus concentration in the surface 10 mm of soil to the concentration of soluble phosphorus in surface runoff.

Table 4:2-3: SWAT+ input variables that pertain to soluble P runoff.

As surface runoff flows over the soil surface, part of the water’s energy is used to pick up and transport soil particles. The smaller particles weigh less and are more easily transported than coarser particles. When the particle size distribution of the transported sediment is compared to that of the soil surface layer, the sediment load to the main channel has a greater proportion of clay sized particles. In other words, the sediment load is enriched in clay particles. Organic nitrogen in the soil is attached primarily to colloidal (clay) particles, so the sediment load will also contain a greater proportion or concentration of organic N than that found in the soil surface layer.

The enrichment ratio is defined as the ratio of the concentration of organic nitrogen transported with the sediment to the concentration in the soil surface layer. SWAT+ will calculate an enrichment ratio for each storm event, or allow the user to define a particular enrichment ratio for organic nitrogen that is used for all storms during the simulation. To calculate the enrichment ratio, SWAT+ uses a relationship described by Menzel (1980) in which the enrichment ratio is logarithmically related to sediment concentration. The equation used to calculate the nitrogen enrichment ratio, $\varepsilon_{N:sed}$, for each storm event is:

$\varepsilon_{N:sed}=0.78*(conc_{sed,surq})^{-0.2468}$ 4:2.2.3

where $conc_{sed,surq}$ is the concentration of sediment in surface runoff (Mg sed/m$^3$ H$_2$O). The concentration of sediment in surface runoff is calculated:

$conc_{sed,surq}=\frac{sed}{10*area_{hru}*Q_{surf}}$ 4:2.2.4

where $sed$ is the sediment yield on a given day (metric tons), $area_{hru}$ is the HRU area (ha), and $Q_{surf}$ is the amount of surface runoff on a given day (mm H$_2$O).

Table 4:2-2: SWAT+ input variables that pertain to organic N loading.

Organic and mineral P attached to soil particles may be transported by surface runoff to the main channel. This form of phosphorus is associated with the sediment loading from the HRU and changes in sediment loading will be reflected in the loading of these forms of phosphorus. The amount of phosphorus transported with sediment to the stream is calculated with a loading function developed by McElroy et al. (1976) and modified by Williams and Hann (1978).

4:2.4.1

where is the amount of phosphorus transported with sediment to the main channel in surface runoff (kg P/ha), is the concentration of phosphorus attached to sediment in the top 10 mm (g P/ metric ton soil), is the sediment yield on a given day (metric tons), is the HRU area (ha), and is the phosphorus enrichment ratio.

The concentration of phosphorus attached to sediment in the soil surface layer, , is calculated:

4:2.4.2

where is the amount of phosphorus in the active mineral pool in the top 10 mm (kg P/ha), is the amount of phosphorus in the stable mineral pool in the top 10 mm (kg P/ha), is the amount of phosphorus in humic organic pool in the top 10 mm (kg P/ha), is the amount of phosphorus in the fresh organic pool in the top 10 mm (kg P/ha), is the bulk density of the first soil layer (Mg/m), and is the depth of the soil surface layer (10 mm).