Reaeration occurs by diffusion of oxygen from the atmosphere into the stream and by the mixing of water and air that occurs during turbulent flow.

The user defines the reaeration rate at 20$\degree$C. The reaeration rate is adjusted to the local water temperature using the relationship:

$\kappa_2=\kappa_{2,20}*1.024^{(T_{water}-20)}$ 7:3.5.4

where $\kappa_2$ is the reaeration rate (day$^{-1}$ or hr$^{-1}$), $\kappa_{2,20}$ is the reaeration rate at 20$\degree$C (day$^{-1}$ or hr$^{-1}$), and $T_{water}$ is the average water temperature for the day or hour ($\degree$C).

Numerous methods have been developed to calculate the reaeration rate at 20$\degree$C, $\kappa_{2,20}$. A few of the methods are listed below. Brown and Barnwell (1987) provide additional methods.

Using field measurements, Churchill, Elmore and Buckingham (1962) derived the relationship:

$\kappa_{2,20}=5.03*v_c^{0.969}*depth^{-1.673}$ 7:3.5.5

where $\kappa_{2,20}$ is the reaeration rate at 20$\degree$C (day$^{-1}$), $v_c$ is the average stream velocity (m/s), and $depth$ is the average stream depth (m).

O’Connor and Dobbins (1958) incorporated stream turbulence characteristics into the equations they developed. For streams with low velocities and isotropic conditions,

$\kappa_{2,20} =294 * \frac{(D_m* v_c)^{0.5}}{depth^{1.5}}$ 7:3.5.6

where $\kappa_{2,20}$ is the reaeration rate at 20$\degree$C (day$^{-1}$), $D_m$ is the molecular diffusion coefficient (m$^2$/day), $v_c$ is the average stream velocity (m/s), and $depth$ is the average stream depth (m). For streams with high velocities and nonisotropic conditions,

$\kappa_{2,20}=2703*\frac{D_m^{0.5}*slp^{0.25}}{depth^{1.25}}$ 7:3.5.7

where $\kappa_{2,20}$ is the reaeration rate at 20$\degree$C (day$^{-1}$), $D_m$ is the molecular diffusion coefficient (m$^2$/day), $slp$ is the slope of the streambed (m/m), and $depth$ is the average stream depth (m). The molecular diffusion coefficient is calculated

$D_m=177*1.037^{\overline T_{water}-20}$ 7:3.5.8

where $D_m$ is the molecular diffusion coefficient (m$^2$/day), and $\overline T_{water}$ is the average water temperature ($\degree$C).

Owens et al. (1964) developed an equation to determine the reaeration rate for shallow, fast moving streams where the stream depth is 0.1 to 3.4 m and the velocity is 0.03 to 1.5 m/s.

$\kappa_{2,20}=5.34*\frac{v_c^{0.67}}{depth^{1.85}}$ 7:3.5.9

where $\kappa_{2,20}$ is the reaeration rate at 20$\degree$C (day$^{-1}$), $v_c$ is the average stream velocity (m/s), and $depth$ is the average stream depth (m).

Reareation will occur when water falls over a dam, weir, or other structure in the stream. To simulate this form of reaeration, a “structure” command line is added in the watershed configuration file (.fig) at every point along the stream where flow over a structure occurs.

The amount of reaeration that occurs is a function of the oxygen deficit above the structure and a reaeration coefficient:

$\Delta Ox_{str}=D_a-D_b=D_a(1-\frac{1}{rea})$ 7:3.5.10

where $\Delta Ox_{str}$ is the change in dissolved oxygen concentration (mg O$_2$/L), $D_a$ is the oxygen deficit above the structure (mg O$_2$/L), $D_b$ is the oxygen deficit below the structure (mg O$_2$/L), and $rea$ is the reaeration coefficient.

The oxygen deficit above the structure, $D_a$, is calculated:

$D_a=Ox_{sat}-Ox_{str}$ 7:3.5.11

where $Ox_{sat}$ is the equilibrium saturation oxygen concentration (mg O$_2$/L), and $Ox_{str}$ is the dissolved oxygen concentration in the stream (mg O$_2$/L).

Butts and Evans (1983) documents the following relationship that can be used to estimate the reaeration coefficient:

$rea=1+0.38*coef_a*coef_b*h_{fall}*(1-0.11*h_{fall})*(1+0.046*\overline T_{water})$ 7:3.5.12

where $rea$ is the reaeration coefficient, $coef_a$ is an empirical water quality factor, $coef_b$ is an empirical dam aeration coefficient, $h_{fall}$ is the height through which water falls (m), and $\overline T_{water}$ is the average water temperature ($\degree$C).

The empirical water quality factor is assigned a value based on the condition of the stream:

$coef_a$ = 1.80 in clean water

$coef_a$ = 1.60 in slightly polluted water

$coef_a$ = 1.00 in moderately polluted water

$coef_a$ = 0.65 in grossly polluted water

The empirical dam aeration coefficient is assigned a value based on the type of structure:

$coef_b$ = 0.70 to 0.90 for flat broad crested weir

$coef_b$ = 1.05 for sharp crested weir with straight slope face

$coef_b$ = 0.80 for sharp crested weir with vertical face

$coef_b$ = 0.05 for sluice gates with submerged discharge

Table 7:3-5: SWAT+ input variables used in in-stream oxygen calculations.