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

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* 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.
* 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_{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>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, 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.
* 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.


Revision as of 13:05, 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:

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_{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 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)} :

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_{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:

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_{c,t} = {\Delta wl_{c,t}}\cdot{ws_{c}}}

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_{c,t}} = The water level change due to the ground bottom flow at 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 t} and 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 c} , 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_{c,t}} = Ground water head at 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 c} and 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 t} .
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 global pressure at 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 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_{c,tf}} = Ground water level (or head pressure) in meters 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} and 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 c} .
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_{c,tf}} = Resistance of the bottom boundary in days 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} and 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 c} .
= Water storage fraction of the soil at 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 c} .
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_{c,t}} = The amount of ground bottom flow through the bottom boundary from deeper ground layers, in m, at 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 t} and 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 c} .

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_{c,t}} 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_{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.
  • 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_{c,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_{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 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 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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