# Nitrate in the Shallow Aquifer

Groundwater flow entering the main channel from the shallow aquifer can contain nitrate. With SWAT+ the nitrate pool in the shallow aquifer is modeled, allowing for fluctuations in nitrate loadings in the groundwater over time.

&#x20;           Nitrate enters the shallow aquifer in recharge from the soil profile. Water that moves past the lowest depth of the soil profile by percolation or bypass flow enters and flows through the vadose zone before becoming shallow and/or deep aquifer recharge. SWAT+ assumes there is no change in nitrate concentration of the recharge as it moves through the vadose zone.

&#x20;           An exponential decay weighting function proposed by Venetis (1969) and used by Sangrey et al. (1984) in a precipitation/groundwater response model is utilized in SWAT+  to account for the time delay in aquifer recharge once the water exits the soil profile. The delay function accommodates situations where the recharge from the soil zone to the aquifer is not instantaneous, i.e. 1 day or less. This same relationship is used to account for the delay in nitrate movement from the soil profile to the aquifers.

The nitrate in recharge to both aquifers on a given day is calculated:

$$NO3_{rchrg,i}=(1-exp\lfloor-1/\delta_{gw}\rfloor)*NO3_{perc}+exp\lfloor-1/\delta_{gw}\rfloor*NO3_{rchrg,i-1}$$

&#x20;                                                                                                3:1.9.1

where $$NO3_{rchrg,i}$$ is the amount of nitrate in recharge entering the aquifers on day $$i$$ (kg N/ha), $$\delta_{gw}$$ is the delay time or drainage time of the overlying geologic formations (days), $$NO3_{perc}$$ is the total amount of nitrate exiting the bottom of the soil profile on day $$i$$ (kg N/ha), and $$NO3_{rchrg,i-1}$$ is the amount of nitrate in recharge entering the aquifers on day $$i-1$$ (mm H$$_2$$O). The total amount of nitrate exiting the bottom of the soil profile on day $$i$$ is calculated using the percolation equation given in Chapter 4:2.

&#x20;       Nitrate in the shallow aquifer may be remain in the aquifer, move with recharge to the deep aquifer, move with groundwater flow into the main channel, or be transported out of the shallow aquifer with water moving into the soil zone in response to water deficiencies. The amount of nitrate in the shallow aquifer after all these processes are taken into account is:

&#x20;     $$NO3_{sh,i}=(NO3_{sh,i-1}+NO3_{rchrg,i})*aq_{sh,i}/(aq_{sh,i}+Q_{gw}+w_{revap}+w_{rchrg,dp})$$

&#x20;                                                                                         3:1.9.2

while the amount of nitrate lost in groundwater flow is

$$NO3_{gw}=(NO3_{sh,i-1}+NO3_{rchrg,i})*Q_{gw}/(aq_{sh,i}+Q_{gw}+w_{revap}+w_{rchrg,dp})$$

&#x20;                                                                                         3:1.9.3

the amount of nitrate lost in revap to the soil profile is

$$NO3_{revap}=(NO3_{sh,i-1}+NO3_{rchrg,i})*w_{revap}/(aq_{sh,i}+Q_{gw}+w_{revap}+w_{rchrg,dp})$$

&#x20;                                                                                       3:1.9.4

and the amount of nitrate transported to the deep aquifer is

$$NO3_{dp}=(NO3_{sh,i-1}+NO3_{rchrg,i})*w_{rchrg,dp}/(aq_{sh,i}+Q_{gw}+w_{revap}+w_{rchrg,dp})$$

&#x20;                                                                                       3:1.9.5

where $$NO3_{sh,i}$$ is the amount of nitrate in the shallow aquifer at the end of day $$i$$ (kg N/ha), $$NO3_{sh,i-1}$$ is the amount of nitrate in the shallow aquifer at the end of day $$i-1$$ (kg N/ha), $$NO3_{rchrg,i}$$ is the amount of nitrate in recharge entering the aquifers on day $$i$$ (kg N/ha), $$NO3_{gw}$$ is the amount of nitrate in groundwater flow from the shallow aquifer on day $$i$$ (kg N/ha), $$NO3_{revap}$$ is the amount of nitrate in revap to the soil profile from the shallow aquifer on day $$i$$ (kg N/ha), $$NO3_{dp}$$ is the amount of nitrate in recharge entering the deep aquifer on day $$i$$ (kg N/ha), $$aq_{sh,i}$$ is the amount of water stored in the shallow aquifer at the end of day $$i$$ (mm H$$_2$$O), $$w_{rchrg}$$ is the amount of recharge entering the aquifers on day $$i$$ (mm H$$_2$$O), $$Q_{gw}$$ is the groundwater flow, or base flow, into the main channel on day $$i$$ (mm H$$_2$$O), $$w_{revap}$$ is the amount of water moving into the soil zone in response to water deficiencies on day $$i$$ (mm H$$_2$$O), and $$w_{rchrg,dp}$$ is the amount of recharge entering the deep aquifer on day $$i$$ (mm H$$_2$$O).

&#x20;   Because nitrogen is a very reactive element, nitrate in the shallow aquifer may be lost due to uptake by bacteria present in the aquifer, chemical transformations driven by a change in redox potential of the aquifer, and other processes. To account for losses of nitrate due to biological and chemical processes, a half-life for nitrate in the aquifer may be defined that specifies the number of days required for a given nitrate concentration to be reduced by one-half. The half-life entered for nitrate in the shallow aquifer is a lumped parameter that includes the net effect of all reactions occurring in the aquifer.

Nitrate removal in the shallow aquifer is governed by first-order kinetics:

$$NO3_{sh,t}=NO3_{sh,o}*exp\lfloor-k_{NO3,sh}*t\rfloor$$                            3:1.9.6

where $$NO3_{sh,t}$$ is the amount of nitrate in the shallow aquifer at time $$t$$ (kg N/ha), $$NO3_{sh,o}$$ is the initial amount of nitrate in the shallow aquifer (kg N/ha), $$k_{NO3,sh}$$ is the rate constant for removal of nitrate in the shallow aquifer (1/day), and $$t$$ is the time elapsed since the initial nitrate amount was determined (days). The rate constant is related to the half-life as follows:

$$t_{1/2,NO3,sh}=\frac{0.693}{k_{NO3,sh}}$$                                                             3:1.9.6

where $$t_{1/2,NO3,sh}$$ is the half-life of nitrate in the shallow aquifer (days).

Table 3:1-5: SWAT+ input variables that pertain to nitrogen in the shallow aquifer.

| Variable Name | Definition                                                             | Input File |
| ------------- | ---------------------------------------------------------------------- | ---------- |
| GW\_DELAY     | $$\delta_{gw}$$: Delay time for aquifer recharge (days)                | .gw        |
| SHALLST\_N    | $$NO3_{sh}$$: Amount of nitrate in the shallow aquifer (kg N/ha)       | .gw        |
| HLIFE\_NGW    | $$t_{1/2,NO3,sh}$$: Half-life of nitrate in the shallow aquifer (days) | .gw        |

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