Reaeration By Turbulent Flow Over A Dam

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.

Variable Name	Definition	File Name
RK2	$\kappa_{2,20}$: Reaeration rate at 20$\degree$C (day$^{-1}$)	.swq
AI3	$\alpha_3$: Rate of oxygen production per unit algal photosynthesis (mg O$_2$/mg alg)	.wwq
AI4	$\alpha_4$: Rate of oxygen uptake per unit algal respiration (mg O$_2$/mg alg)	.wwq
RHOQ	$\rho_{a,20}$: Local algal respiration rate at 20$\degree$C (day$^{-1}$)	.wwq
RK1	$\kappa_{1,20}$: CBOD deoxygenation rate at 20$\degree$C (day$^{-1}$)	.swq
RK4	$\kappa_{4,20}$:Sediment oxygen demand rate at 20$\degree$C(mg O$_2$/(m$^2$.day))	.swq
AI5	$\alpha_5$: Rate of oxygen uptake per unit NH$_4^+$ oxidation (mg O$_2$/mg N)	.wwq
AI6	$\alpha_6$: Rate of oxygen uptake per unit NO$_2$ oxidation (mg O$_2$/mg N)	.wwq
AERATION_COEF	$rea$: Reaeration coefficient	.fig