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

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:

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} .

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.
$p_{c,tf}$ 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)

References

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

Models

Surface • Ground • Rain • Evaporation • Infiltration • Elevation • Breach • Sewer • Storage • Tracer flow • Border • Order
Model formulas

Timestep • Season • Surface water level • Groundwater level
Flow formulas

Surface flow • Surface infiltration • Ground flow • Ground infiltration • Surface evaporation • Ground evaporation • Ground bottom flow
Hydraulic structure formulas

Culvert • Weir • Breach growth • Breach flow • Pump • Sewer Overflow • Inlet • Drainage
Related

Building attributes • Hydrological features • Hydraulic structures • Terrain attributes • Model attributes • Results • Simulation data

[pankow-1] Estimating ground bottom flow, http://grondwaterformules.nl/index.php/formules/ontwatering/kwel-berekenen-pankow, last visited on 2-9-2020

[1]

@@ Line 1: / Line 1: @@
-Underground seepage (from (or to) outside the project area) is calculated per cell.
+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 />.
+__NOTOC__
+The water level change due to ground bottom flow is calculated using the following formula:
+: <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 seepage is calculated using the following formula:
+The external bottom head pressure is variable over time by the introduction of <math>h_{v}(t)</math>:
-: <math>\Delta s = \frac{h_{d}(t) - h_{x,y}}{c} \cdot \frac{\Delta t}{24 \cdot 60 \cdot 60}</math>
+: <math>h_d(t) = p_{c,tf} + h_{v}(t)</math>
-The external seepage head is variable over time by the introduction of h<sub>v,t</sub>
+Finally, the actual amount of water flowing into the ground from the deeper ground layers through the bottom boundary is calculated as followed:
-: <math>h_d(t) = h_c + h_{v,t}(t)</math>
+: <math>\Delta s_{c,t} = {\Delta wl_{c,t}}\cdot{ws_{c}}</math>
-Finally, calculate the actual amount of water seeping into (or out of) the ground from the bottom.
+where:
-: <math>\Delta w = \frac{\Delta s}{ws}</math>
+: <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>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 bottom pressure m (Water Overlay)|global pressure]] at time <math>t</math>, in meters.
+: <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>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_{c}</math> = [[Terrain water storage percentage (Water Overlay)|Water storage fraction]] of the soil at cell <math>c</math>.
+: <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>.
-Where:
+{{article end
-* <math>\Delta s</math> = The underground seepage which takes place, in meters.
+|notes=
-* <math>\Delta t</math> = Computational timestep in seconds.
+* 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>h_{x,y}</math> = Ground water head in the grid cell.
+* <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_{d,t}</math> = ground water level (or head) of the external zone causing the seepage at time t, in meters
+* [[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.
-* <math>h_{c}</math> = constant ground water level (or head) of the external zone causing the seepage, in meters
+* 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.
-* <math>h_{v,t}</math> = additional variation of seepage head over time
-* <math>c</math> = resistance of the separating layer in days
-* <math>ws</math> = water storage fraction of the soil
-==Related==
+|related=
 The following topics are related to this formula.
 ; Formulas
-: [[Groundwater level formula (Water Overlay)|Groundwater level formula]]
+: [[Groundwater level formula (Water Overlay)]]
-: [[Surface infiltration formula (Water Overlay)|Surface infiltration formula]]
 ; Models
-: [[Underground model (Water Overlay)|Underground model]]
+: [[Ground model (Water Overlay)]]
-: [[Infiltration model (Water Overlay)|Infiltration model]]
+|seealso=
+* [[Bottom pressure prequel (Water Overlay)]]
+* [[Bottom resistance prequel (Water Overlay)]]
+* [[Ground bottom flow result type (Water Overlay)]]
+* [[Ground bottom pressure m (Water Overlay)]]
+|howtos=
+* [[How to configure constant bottom boundary flow (Water Overlay)]]
+|references=<references>
+<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>
+}}
-==See also==
+{{WaterOverlay formula nav}}
-* The formula is based on the formula of Pankow for [http://grondwaterformules.nl/index.php/formules/ontwatering/kwel-berekenen-pankow  estimating seepage]
-{{Template:WaterOverlay_nav}}

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

Latest revision as of 13:06, 27 February 2024

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