Ground bottom flow formula (Water Overlay)

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.

The water level change due to ground bottom flow is calculated using the following formula:

$\Delta wl_{c,t}={\frac {h_{d}(t)-h_{c,t}}{c_{c,tf}}}\cdot {\frac {\Delta t}{24\cdot 60\cdot 60}}$

The external bottom head pressure is variable over time by the introduction of $h_{v}(t)$:

$h_{d}(t)=p_{c,tf}+h_{v}(t)$

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

$\Delta s_{c,t}={\Delta wl_{c,t}}\cdot {ws_{c}}$

where:

$\Delta wl_{c,t}$ = The water level change due to the ground bottom flow at time $t$ and cell $c$, in meters.

$\Delta t$ = Computational timestep in seconds.

$h_{c,t}$ = Ground water head at cell $c$ and time $t$.

$h_{d}(t)$ = Additional global pressure at time $t$, in meters.

$p_{c,tf}$ = Ground water level (or head pressure) in meters at timeframe $tf$ and cell $c$.

$h_{v}(t)$ = Additional variation of bottom head pressure over time.

$c_{c,tf}$ = Resistance of the bottom boundary in days at timeframe $tf$ and cell $c$.

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 ws_{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 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

• How to configure constant bottom boundary flow (Water Overlay)

Related

The following topics are related to this formula.

Formulas

Groundwater level formula (Water Overlay)

Models

Ground model (Water Overlay)

See also

• Bottom pressure prequel (Water Overlay)
• Bottom resistance prequel (Water Overlay)
• Ground bottom flow result type (Water Overlay)
• Ground bottom pressure m (Water Overlay)

References

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