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

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[[File:YoutubeLogo1.jpg|thumb|left|link=https://youtu.be/SODR9XlYTfo|Hoe is kwel geïmplementeerd in het Tygron Geodesign Platform? (Dutch only)]]
[[File:YoutubeLogo1.jpg|thumb|left|link=https://youtu.be/SODR9XlYTfo|Hoe is kwel geïmplementeerd in het Tygron Geodesign Platform? (Dutch only)]]
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Ground bottom flow 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 />.
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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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_{x,y} = \frac{h_{d}(t) - h_{x,y}}{c_{x,y,tf}} \cdot \frac{\Delta t}{24 \cdot 60 \cdot 60}</math>


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where:
where:
: <math>\Delta wl_{x,y}</math> = The water level change due to seepage, in meters.
: <math>\Delta wl_{x,y}</math> = The water level change due to the ground bottom flow, 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_{x,y}</math> = [[Groundwater level formula (Water Overlay)|Ground water head]] in the grid cell.

Revision as of 16:25, 26 January 2024

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

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_{x,y} = \frac{h_{d}(t) - h_{x,y}}{c_{x,y,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_{x,y,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_{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 the ground bottom flow, 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 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} .
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,tf}} = Resistance of the separating layer 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}
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 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_{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,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.
  • 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
Ground 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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