Suspended algal biomass is assumed to be directly proportional to chlorophyll $a$. Therefore, the algal biomass loading to the stream can be estimated as the chlorophyll $a$ loading from the land area. Cluis et al. (1988) developed a relationship between the nutrient enrichment index (total N: total P), chlorophyll $a$, and algal growth potential in the North Yamaska River, Canada.

$(AGP+chla)*v_{surf}=f*(\frac{TN}{TP})^g$ 4:5.1.1

where $AGP$ is the algal growth potential (mg/L), $chla$ is the chlorophyll $a$ concentration in the surface runoff ($\mu g$/L), $v_{surf}$ is the surface runoff flow rate (m$^3$/s), $TN$ is the total Kjeldahl nitrogen load (kmoles), $TP$ is the total phosphorus load (kmoles), $f$ is a coefficient and $g$ is an exponent.

The chlorophyll concentration in surface runoff is calculated in SWAT+ using a simplified version of Cluis et al.’s exponential function (1988):

if or and 4:5.1.2

if or ( and ) 4:5.1.3

if , and 4:5.1.4

In addition to sediment, nutrients, and pesticides, SWAT+ will calculate the amount of algae, dissolved oxygen and carbonaceous biological oxygen demand (CBOD) entering the main channel with surface runoff. Loadings of these three parameters impact the quality of stream water. This chapter reviews the algorithms governing movement of algae, dissolved oxygen and CBOD from land areas to the stream network. Because the algorithms were based on very limited field data, calculation of these loadings has been made optional.

Rainfall is assumed to be saturated with oxygen. To determine the dissolved oxygen concentration of surface runoff, the oxygen uptake by the oxygen demanding substance in runoff is subtracted from the saturation oxygen concentration.

$Ox_{surf}=Ox_{sat}-\kappa_1*cbod_{surq}*\frac{t_{ov}}{24}$ 4:5.3.1

where $Ox_{surf}$ is the dissolved oxygen concentration in surface runoff (mg $O_2$/L), $Ox_{sat}$ is the saturation oxygen concentration (mg $O_2$/L), $\kappa_1$ is the CBOD deoxygenation rate (day$^{-1}$), $cbod_{surq}$ is the CBOD concentration in surface runoff (mg CBOD/L), and $t_{ov}$ is the time of concentration for overland flow (hr). For loadings from HRUs, SWAT+ assumes $\kappa_1$ = 1.047 day$^{-1}$.

The amount of oxygen that can be dissolved in water is a function of temperature, concentration of dissolved solids, and atmospheric pressure. An equation developed by APHA (1985) is used to calculate the saturation concentration of dissolved oxygen:

$Ox_{sat}=exp[-139.34410+\frac{1.575701*10^5}{T_{wat,K}}-\frac{6.642308*10^7}{(T_{wat,K})^2}+\frac{1.243800*10^{10}}{(T_{wat,K})^3}-\frac{8.621949*10^{11}}{(T_{wat,K})^4}]$

4:5.3.2

where $Ox_{sat}$ is the equilibrium saturation oxygen concentration at 1.00 atm (mg $O_2$/L), and $T_{wat,K}$ is the water temperature in Kelvin (273.15+°C).

Carbonaceous biological oxygen demand (CBOD) defines the amount of oxygen required to decompose the organic matter transported in surface runoff. The SWAT+ loading function for CBOD is based on a relationship given by Thomann and Mueller (1987):

$cbod_{surq}=\frac{2.7*orgC_{surq}}{Q_{surf}*area_{hru}}$ 4:5.2.1

where $cbod_{surq}$ is the CBOD concentration in surface runoff (mg CBOD/L), $orgC_{surq}$ is the organic carbon in surface runoff (kg $orgC$), $Q_{surf}$ is the surface runoff on a given day (mm H$_2$O), and $area_{hru}$ is the area of the HRU (km$^2$).

The amount of organic carbon in surface runoff is calculated:

4:5.2.2

where is the organic carbon in surface runoff (kg ), is the percent organic carbon in the top 10 mm of soil (%), is the sediment loading from the HRU (metric tons), and is the carbon enrichment ratio.

As 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 carbon in the soil is attached primarily to colloidal (clay) particles, so the sediment load will also contain a greater proportion or concentration of organic carbon than that found in the soil surface layer.

The enrichment ratio is defined as the ratio of the concentration of organic carbon transported with the sediment to the concentration in the soil surface layer. SWAT+ will calculate an enrichment ratio for each storm event. 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 carbon enrichment ratio, $\varepsilon_{C:sed}$, for each storm event is:

$\varepsilon_{C:sed}=0.78*(conc_{sed,surq})^{-0.2468}$ 4:5.2.3

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

4:5.2.4

where is the sediment yield on a given day (metric tons), is the HRU area (ha), and is the amount of surface runoff on a given day (mm HO).

Table 4:5-1: SWAT+ input variables that pertain to CBOD in surface runoff.