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

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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<ref name=pankow />.
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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<ref name=pankow />.
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The water level change due to seepage 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,t} = \frac{h_{d}(t) - h_{c,t}}{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 seeping into the ground from the bottom 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,t} = {\Delta wl_{c,t}}\cdot{ws_{c}}</math>


where:
where:
: <math>\Delta wl_{x,y}</math> = The water level change due to seepage, in meters.
: <math>\Delta wl_{c,t}</math> = The water level change due to the ground bottom flow at time <math>t</math> and 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,t}</math> = [[Groundwater level formula (Water Overlay)|Ground water head]] at cell <math>c</math> and time <math>t</math>.
: <math>h_{d}(t)</math> = Additional ground water level (or head) of the external zone causing the seepage at time t, in meters
: <math>h_{d}(t)</math> = Additional [[Ground bottom pressure m (Water Overlay)|global pressure]] at time <math>t</math>, in meters.
: <math>p_{x,y,tf}</math> = [[Bottom pressure prequel (Water Overlay)#Bottom pressure|Ground water level (or head) of the external zone]] 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> and cell <math>c</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 separating layer]] 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> and cell <math>c</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 at cell <math>c</math>.
: <math>\Delta s_{x,y}</math> = Seeped in water in m
: <math>\Delta s_{c,t}</math> = The amount of ground bottom flow through the bottom boundary from deeper ground layers, in m, at time <math>t</math> and cell <math>c</math>.


{{article end
{{article end
|notes=
|notes=
* The calculated <math>\Delta wl_{x,y}</math> is essentially the change in groundwater level, inherently taking into account the porosity of the soil. The final <math>\Delta s_{x,y}</math> 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.
* The calculated <math>\Delta wl_{c,t}</math> is essentially the change in groundwater level, inherently taking into account the porosity of the soil. The final <math>\Delta s_{c}</math> 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.
* <math>p_{x,y,tf}</math> and <math>c_{x,y,tf}</math> can both be provided as spatially variable values using [[Prequels (Water Overlay)|prequel overlay]]s. These prequels can have multiple timeframes, as indicated by the formula, allowing changing head and resistances over time.
* <math>p_{c,tf}</math> and <math>c_{c,tf}</math> can both be provided as spatially variable values using [[Prequels (Water Overlay)|prequel overlay]]s. These prequels can have multiple timeframes, as indicated by the formula, allowing changing head and resistances over time.
* <math>h_{v}(t)</math> can be provided as a set of values, variable over time.
* [[Groundwater level formula (Water Overlay)|Ground water head]] <math>h_{v}(t)</math> can be provided as a set of values that variate 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.
* 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=
|related=
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: [[Groundwater level formula (Water Overlay)]]
: [[Groundwater level formula (Water Overlay)]]
; Models
; Models
: [[Underground model (Water Overlay)]]
: [[Ground model (Water Overlay)]]
|seealso=
|seealso=
* [[Bottom pressure prequel (Water Overlay)]]
* [[Bottom pressure prequel (Water Overlay)]]
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* [[Ground bottom pressure m (Water Overlay)]]
* [[Ground bottom pressure m (Water Overlay)]]
|howtos=
|howtos=
* [[How to configure constant seepage (Water Overlay)]]
* [[How to configure constant bottom boundary flow (Water Overlay)]]
|references=<references>
|references=<references>
<ref name=pankow>Estimating seepage, http://grondwaterformules.nl/index.php/formules/ontwatering/kwel-berekenen-pankow, last visited on 2-9-2020</ref>
<ref name=pankow>Estimating ground bottom flow, http://grondwaterformules.nl/index.php/formules/ontwatering/kwel-berekenen-pankow, last visited on 2-9-2020</ref>
</references>
</references>
}}
}}


{{WaterOverlay formula nav}}
{{WaterOverlay formula nav}}

Latest revision as of 13:06, 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 time and cell , in meters.
= Computational timestep in seconds.
= Ground water head at cell and time .
= Additional global pressure at time , in meters.
= Ground water level (or head pressure) in meters at timeframe and cell .
= Additional variation of bottom head pressure over time.
= Resistance of the bottom boundary in days at timeframe and cell .
= Water storage fraction of the soil at cell .
= The amount of ground bottom flow through the bottom boundary from deeper ground layers, in m, at time and cell .

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.
  • Ground water head 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.

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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