Ground bottom flow formula (Water Overlay): Difference between revisions

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The water level change due to ground bottom flow is calculated using the following formula:
The water level change due to ground bottom flow is calculated using the following formula:
: <math>\Delta wl_{x,y} = \frac{h_{d}(t) - h_{x,y}}{c_{x,y,tf}} \cdot \frac{\Delta t}{24 \cdot 60 \cdot 60}</math>
: <math>\Delta wl_{c} = \frac{h_{d}(t) - h_{c}}{c_{c,tf}} \cdot \frac{\Delta t}{24 \cdot 60 \cdot 60}</math>


The external bottom head pressure is variable over time by the introduction of <math>h_{v}(t)</math>:
The external bottom head pressure is variable over time by the introduction of <math>h_{v}(t)</math>:
: <math>h_d(t) = p_{x,y,tf} + h_{v}(t)</math>
: <math>h_d(t) = p_{c,tf} + h_{v}(t)</math>


Finally, the actual amount of water flowing into the ground from the deeper ground layers through the bottom boundary is calculated as followed:
Finally, the actual amount of water flowing into the ground from the deeper ground layers through the bottom boundary is calculated as followed:
: <math>\Delta s_{x,y} = {\Delta wl_{x,y}}\cdot{ws}</math>
: <math>\Delta s_{c} = {\Delta wl_{c}}\cdot{ws_{c}}</math>


where:
where:
: <math>\Delta wl_{x,y}</math> = The water level change due to the ground bottom flow, in meters.
: <math>\Delta wl_{c}</math> = The water level change due to the ground bottom flow at cell <math>c</math>, in meters.
: <math>\Delta t</math> = Computational timestep in seconds.
: <math>\Delta t</math> = Computational timestep in seconds.
: <math>h_{x,y}</math> = [[Groundwater level formula (Water Overlay)|Ground water head]] in the grid cell.
: <math>h_{c}</math> = [[Groundwater level formula (Water Overlay)|Ground water head]] at cell <math>c</math>.
: <math>h_{d}(t)</math> = Additional [[Ground bottom pressure m (Water Overlay)|global pressure]] at time t, in meters
: <math>h_{d}(t)</math> = Additional [[Ground bottom pressure m (Water Overlay)|global pressure]] at time t, in meters
: <math>p_{x,y,tf}</math> = [[Bottom pressure prequel (Water Overlay)#Bottom pressure|Ground water level (or head pressure)]] in meters at [[Timeframes (Water Overlay)|timeframe]] <math>tf</math>.
: <math>p_{c,tf}</math> = [[Bottom pressure prequel (Water Overlay)#Bottom pressure|Ground water level (or head pressure)]] in meters at [[Timeframes (Water Overlay)|timeframe]] <math>tf</math>.
: <math>h_{v}(t)</math> = [[Ground bottom pressure m (Water Overlay)|Additional variation of bottom head pressure]] over time
: <math>h_{v}(t)</math> = [[Ground bottom pressure m (Water Overlay)|Additional variation of bottom head pressure]] over time
: <math>c_{x,y,tf}</math> = [[Bottom resistance prequel (Water Overlay)#Bottom resistance|Resistance of the bottom boundary]] in days at [[Timeframes (Water Overlay)|timeframe]] <math>tf</math>
: <math>c_{c,tf}</math> = [[Bottom resistance prequel (Water Overlay)#Bottom resistance|Resistance of the bottom boundary]] in days at [[Timeframes (Water Overlay)|timeframe]] <math>tf</math>
: <math>ws</math> = [[Terrain water storage percentage (Water Overlay)|Water storage fraction]] of the soil
: <math>ws_{c}</math> = [[Terrain water storage percentage (Water Overlay)|Water storage fraction]] of the soil
: <math>\Delta s_{x,y}</math> = Water flowed in through the bottom boundary from deeper ground layers, in m
: <math>\Delta s_{c}</math> = Water flowed in through the bottom boundary from deeper ground layers, in m


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Revision as of 12:56, 27 February 2024

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:

The external bottom head pressure is variable over time by the introduction of :

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

where:

= The water level change due to the ground bottom flow at cell , in meters.
= Computational timestep in seconds.
= Ground water head at cell .
= Additional global pressure at time t, in meters
= Ground water level (or head pressure) in meters at timeframe .
= Additional variation of bottom head pressure over time
= Resistance of the bottom boundary in days at timeframe
= Water storage fraction of the soil
= Water flowed in through the bottom boundary from deeper ground layers, in m

Notes

  • The calculated is essentially the change in groundwater level, inherently taking into account the porosity of the soil. The final 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.
  • and 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.
  • can be provided as a set of values, variable over time.
  • A head pressure lower than the water level in the project is also allowed, resulting in ground water lowering and flowing into the deeper ground layers and out of the project area.

How-to's

Related

The following topics are related to this formula.

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

See also

References

  1. ↑ Estimating ground bottom flow, http://grondwaterformules.nl/index.php/formules/ontwatering/kwel-berekenen-pankow, last visited on 2-9-2020
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