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).