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

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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) = h_{p_{x,y}} + h_{v}(t)</math>
: <math>h_d(t) = p_{x,y,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 seeping into the ground from the bottom is calculated as followed:
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: <math>h_{x,y}</math> = [[Groundwater level formula (Water Overlay)|Ground water head]] in the grid cell.
: <math>h_{x,y}</math> = [[Groundwater level formula (Water Overlay)|Ground water head]] in the grid cell.
: <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 water level (or head) of the external zone causing the seepage at time t, in meters
: <math>h_{p_{x,y,tf}}</math> = [[Bottom pressure prequel (Water Overlay)#Bottom pressure|Ground water level (or head) of the external zone]] causing the seepage at [[Timeframes (Water Overlay)|timeframe]] <math>tf</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]] causing the seepage at [[Timeframes (Water Overlay)|timeframe]] <math>tf</math>, in meters
: <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}</math> = [[Bottom resistance prequel (Water Overlay)#Bottom resistance|Resistance of the separating layer]] in days
: <math>c_{x,y}</math> = [[Bottom resistance prequel (Water Overlay)#Bottom resistance|Resistance of the separating layer]] in days

Revision as of 15:46, 25 January 2024

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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[1].

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

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

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle h_d(t) = p_{x,y,tf} + h_{v}(t)}

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

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Delta s_{x,y} = {\Delta wl_{x,y}}\cdot{ws}}

where:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Delta wl_{x,y}} = The water level change due to seepage, in meters.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Delta t} = Computational timestep in seconds.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle h_{x,y}} = Ground water head in the grid cell.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle h_{d}(t)} = Additional ground water level (or head) of the external zone causing the seepage at time t, in meters
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p_{x,y,tf}} = Ground water level (or head) of the external zone causing the seepage at timeframe Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle tf} , in meters
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle h_{v}(t)} = Additional variation of bottom head pressure over time
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c_{x,y}} = Resistance of the separating layer in days
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle ws} = Water storage fraction of the soil
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Delta s_{x,y}} = Seeped in water in m

Notes

  • The calculated Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Delta wl_{x,y}} is essentially the change in groundwater level, inherently taking into account the porosity of the soil. The final Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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.
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle h_{p_{x,y,tf}}} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle c_{x,y}} can both be provided as spatially variable values.
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\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.

How-to's

Related

The following topics are related to this formula.

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

See also

References

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