# Ground bottom flow formula (Water Overlay)

Ground water flowing in from deeper ground layers through the bottom boundary, due to head pressure from water bodies situated outside the project area is calculated per grid cell. The formula is based on the principles used in the formula of Pankow for estimating this ground bottom flow[1].

The water level change due to ground bottom flow is calculated using the following formula:

${\displaystyle \Delta wl_{c,t}={\frac {h_{d}(t)-h_{c,t}}{c_{c,tf}}}\cdot {\frac {\Delta t}{24\cdot 60\cdot 60}}}$

The external bottom head pressure is variable over time by the introduction of ${\displaystyle h_{v}(t)}$:

${\displaystyle h_{d}(t)=p_{c,tf}+h_{v}(t)}$

Finally, the actual amount of water flowing into the ground from the deeper ground layers through the bottom boundary is calculated as followed:

${\displaystyle \Delta s_{c,t}={\Delta wl_{c,t}}\cdot {ws_{c}}}$

where:

${\displaystyle \Delta wl_{c,t}}$ = The water level change due to the ground bottom flow at time ${\displaystyle t}$ and cell ${\displaystyle c}$, in meters.
${\displaystyle \Delta t}$ = Computational timestep in seconds.
${\displaystyle h_{c,t}}$ = Ground water head at cell ${\displaystyle c}$ and time ${\displaystyle t}$.
${\displaystyle h_{d}(t)}$ = Additional global pressure at time ${\displaystyle t}$, in meters.
${\displaystyle p_{c,tf}}$ = Ground water level (or head pressure) in meters at timeframe ${\displaystyle tf}$ and cell ${\displaystyle c}$.
${\displaystyle h_{v}(t)}$ = Additional variation of bottom head pressure over time.
${\displaystyle c_{c,tf}}$ = Resistance of the bottom boundary in days at timeframe ${\displaystyle tf}$ and cell ${\displaystyle c}$.
${\displaystyle ws_{c}}$ = Water storage fraction of the soil at cell ${\displaystyle c}$.
${\displaystyle \Delta s_{c,t}}$ = The amount of ground bottom flow through the bottom boundary from deeper ground layers, in m, at time ${\displaystyle t}$ and cell ${\displaystyle c}$.

## Notes

• The calculated ${\displaystyle \Delta wl_{c,t}}$ is essentially the change in groundwater level, inherently taking into account the porosity of the soil. The final ${\displaystyle \Delta s_{c}}$ is representative of the actual amount of water, i.e. the height of the water, if the relevant quantity of water wasn't in the ground but sat on the surface instead.
• ${\displaystyle p_{c,tf}}$ and ${\displaystyle c_{c,tf}}$ can both be provided as spatially variable values using prequel overlays. These prequels can have multiple timeframes, as indicated by the formula, allowing changing head and resistances over time.
• Ground water head ${\displaystyle h_{v}(t)}$ can be provided as a set of values that variate over time.
• A head pressure lower than the water level in the project is also allowed, resulting in a lowering of the ground water level, with water flowing into the deeper ground layers and out of the project area.

## Related

The following topics are related to this formula.

Formulas
Groundwater level formula (Water Overlay)
Models
Ground model (Water Overlay)