# Underground seepage formula (Water Overlay)

Hoe is kwel geïmplementeerd in het Tygron Geodesign Platform? (Dutch only)

Underground seepage from outside the project area is calculated per grid cell. The formula is based on the principles used in the formula of Pankow for estimating seepage[1].

The water level change due to seepage is calculated using the following formula:

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

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

${\displaystyle h_{d}(t)=h_{p_{x,y}}+h_{v}(t)}$

Finally, the actual amount of water seeping into the ground from the bottom is calculated as followed:

${\displaystyle \Delta s_{x,y}={\Delta wl_{x,y}}\cdot {ws}}$

where:

${\displaystyle \Delta wl_{x,y}}$ = The water level change due to seepage, in meters.
${\displaystyle \Delta t}$ = Computational timestep in seconds.
${\displaystyle h_{x,y}}$ = Ground water head in the grid cell.
${\displaystyle h_{d}(t)}$ = Additional ground water level (or head) of the external zone causing the seepage at time t, in meters
${\displaystyle h_{p_{x,y}}}$ = Constant ground water level (or head) of the external zone causing the seepage, in meters
${\displaystyle h_{v}(t)}$ = Additional variation of seepage head over time
${\displaystyle c_{x,y}}$ = Resistance of the separating layer in days
${\displaystyle ws}$ = Water storage fraction of the soil
${\displaystyle \Delta s_{x,y}}$ = Seeped in water in m

## Notes

• The calculated ${\displaystyle \Delta wl_{x,y}}$ is essentially the change in groundwater level, inherently taking into account the porosity of the soil. The final ${\displaystyle \Delta s_{x,y}}$ 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 underground but sat on the surface instead.
• ${\displaystyle h_{p_{x,y}}}$ and ${\displaystyle c_{x,y}}$ can both be provided as spatially variable values.
• ${\displaystyle h_{v}(t)}$ can be provided as a set of values, variable over time.
• A seepage head lower than the water level in the project is also allowed, resulting in water seeping out to a region outside the project area.

## Related

The following topics are related to this formula.

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