Ground bottom flow formula (Water Overlay) - Revision history

Rudolf@tygron.nl at 14:09, 17 October 2025

2025-10-17T14:09:43Z

← Older revision		Revision as of 14:09, 17 October 2025
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	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 />.		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\|pankow}}.
	__NOTOC__		__NOTOC__
	The water level change due to ground bottom flow is calculated using the following formula:		The water level change due to ground bottom flow is calculated using the following formula:
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	* [[How to configure constant bottom boundary flow (Water Overlay)]]		* [[How to configure constant bottom boundary flow (Water Overlay)]]
	\|references=<references>		\|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>~~		{{ref\|pankow
			\|name=Estimating ground bottom flow
			\|author=
			\|page=
			\|source=
			\|link=http://grondwaterformules.nl/index.php/formules/ontwatering/kwel-berekenen-pankow
			\|lastvisit=2020-09-02
			}}
	</references>		</references>
	}}		}}

	{{WaterOverlay formula nav}}		{{WaterOverlay formula nav}}

Frank@tygron.nl at 13:06, 27 February 2024

2024-02-27T13:06:38Z

← Older revision		Revision as of 13:06, 27 February 2024
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	* <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.
	* [[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.		* [[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.
	* 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 a lowering of the ground water level, with water flowing into the deeper ground layers and out of the project area.

	\|related=		\|related=

Frank@tygron.nl at 13:05, 27 February 2024

2024-02-27T13:05:41Z

← Older revision		Revision as of 13:05, 27 February 2024
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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.
	* [[Groundwater level formula (Water Overlay)\|Ground water head]] <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 that variate 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.

Frank@tygron.nl at 13:05, 27 February 2024

2024-02-27T13:05:11Z

← Older revision		Revision as of 13:05, 27 February 2024
Line 25:		Line 25:
	* 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.

Frank@tygron.nl at 13:04, 27 February 2024

2024-02-27T13:04:43Z

← Older revision		Revision as of 13:04, 27 February 2024
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	: <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_{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>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.		: <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>.		: <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>.

	{{article end		{{article end
	\|notes=		\|notes=
	* The calculated <math>\Delta wl_{c}</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.		* <math>h_{v}(t)</math> can be provided as a set of values, variable over time.

Frank@tygron.nl at 13:03, 27 February 2024

2024-02-27T13:03:47Z

Frank@tygron.nl at 13:02, 27 February 2024

2024-02-27T13:02:00Z

Frank@tygron.nl at 12:59, 27 February 2024

2024-02-27T12:59:11Z

← Older revision		Revision as of 12:59, 27 February 2024
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	{{article end		{{article end
	\|notes=		\|notes=
	* The calculated <math>\Delta wl_{~~x,y~~}</math> is essentially the change in groundwater level, inherently taking into account the porosity of the soil. The final <math>\Delta s_{~~x,y~~}</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}</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_{~~x,y~~,tf}</math> and <math>c_{~~x,y~~,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.		* <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.

Frank@tygron.nl at 12:56, 27 February 2024

2024-02-27T12:56:38Z

Frank@tygron.nl at 08:52, 29 January 2024

2024-01-29T08:52:06Z

← Older revision		Revision as of 08:52, 29 January 2024
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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)]]~~
	~~{{clear}}~~
	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 />.		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__		__NOTOC__

← Older revision		Revision as of 13:03, 27 February 2024
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	__NOTOC__		__NOTOC__
	The water level change due to ground bottom flow is calculated using the following formula:		The water level change due to ground bottom flow is calculated using the following formula:
	: <math>\Delta wl_{c} = \frac{h_{d}(t) - h_{c}}{c_{c,tf}} \cdot \frac{\Delta t}{24 \cdot 60 \cdot 60}</math>		: <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 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>:
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	Finally, the actual amount of water flowing into the ground from the deeper ground layers through the bottom boundary is calculated as followed:		Finally, the actual amount of water flowing into the ground from the deeper ground layers through the bottom boundary is calculated as followed:
	: <math>\Delta s_{c,t} = {\Delta wl_{c}}\cdot{ws_{c}}</math>		: <math>\Delta s_{c,t} = {\Delta wl_{c,t}}\cdot{ws_{c}}</math>

	where:		where:
	: <math>\Delta wl_{c}</math> = The water level change due to the ground bottom flow at cell <math>c</math>, in meters.		: <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>\Delta t</math> = Computational timestep in seconds.
	: <math>h_{c}</math> = [[Groundwater level formula (Water Overlay)\|Ground water head]] at cell <math>c</math>.		: <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 t, in meters.		: <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>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>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>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.		: <math>ws_{c}</math> = [[Terrain water storage percentage (Water Overlay)\|Water storage fraction]] of the soil.
	: <math>\Delta s_{c,t}</math> = The amount of ground bottom flow ~~hrough~~ the bottom boundary from deeper ground layers, in m and 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>.

	{{article end		{{article end

← Older revision		Revision as of 13:02, 27 February 2024
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	Finally, the actual amount of water flowing into the ground from the deeper ground layers through the bottom boundary is calculated as followed:		Finally, the actual amount of water flowing into the ground from the deeper ground layers through the bottom boundary is calculated as followed:
	: <math>\Delta s_{c} = {\Delta wl_{c}}\cdot{ws_{c}}</math>		: <math>\Delta s_{c,t} = {\Delta wl_{c}}\cdot{ws_{c}}</math>

	where:		where:
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	: <math>\Delta t</math> = Computational timestep in seconds.		: <math>\Delta t</math> = Computational timestep in seconds.
	: <math>h_{c}</math> = [[Groundwater level formula (Water Overlay)\|Ground water head]] at cell <math>c</math>.		: <math>h_{c}</math> = [[Groundwater level formula (Water Overlay)\|Ground water head]] at cell <math>c</math>.
	: <math>h_{d}(t)</math> = Additional [[Ground bottom pressure m (Water Overlay)\|global pressure]] at time t, in meters		: <math>h_{d}(t)</math> = Additional [[Ground bottom pressure m (Water Overlay)\|global pressure]] at time t, 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>.		: <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>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>		: <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		: <math>ws_{c}</math> = [[Terrain water storage percentage (Water Overlay)\|Water storage fraction]] of the soil.
	: <math>\Delta s_{c}</math> = ~~Water flowed in through~~ the bottom boundary from deeper ground layers, in m		: <math>\Delta s_{c,t}</math> = The amount of ground bottom flow hrough the bottom boundary from deeper ground layers, in m and at cell <math>c</math>.

	{{article end		{{article end

← Older revision		Revision as of 12:56, 27 February 2024
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	__NOTOC__		__NOTOC__
	The water level change due to ground bottom flow 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_{c} = \frac{h_{d}(t) - h_{c}}{c_{c,tf}} \cdot \frac{\Delta t}{24 \cdot 60 \cdot 60}</math>

	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) = p_{~~x,y~~,tf} + h_{v}(t)</math>		: <math>h_d(t) = p_{c,tf} + h_{v}(t)</math>

	Finally, the actual amount of water flowing into the ground from the deeper ground layers through the bottom boundary is calculated as followed:		Finally, the actual amount of water flowing into the ground from the deeper ground layers through the bottom boundary is calculated as followed:
	: <math>\Delta s_{~~x,y~~} = {\Delta wl_{~~x,y~~}}\cdot{ws}</math>		: <math>\Delta s_{c} = {\Delta wl_{c}}\cdot{ws_{c}}</math>

	where:		where:
	: <math>\Delta wl_{~~x,y~~}</math> = The water level change due to the ground bottom flow, in meters.		: <math>\Delta wl_{c}</math> = The water level change due to the ground bottom flow at cell <math>c</math>, 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_{c}</math> = [[Groundwater level formula (Water Overlay)\|Ground water head]] at cell <math>c</math>.
	: <math>h_{d}(t)</math> = Additional [[Ground bottom pressure m (Water Overlay)\|global pressure]] at time t, in meters		: <math>h_{d}(t)</math> = Additional [[Ground bottom pressure m (Water Overlay)\|global pressure]] at time t, in meters
	: <math>p_{~~x,y~~,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>.		: <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>.
	: <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~~,tf}</math> = [[Bottom resistance prequel (Water Overlay)#Bottom resistance\|Resistance of the bottom boundary]] in days at [[Timeframes (Water Overlay)\|timeframe]] <math>tf</math>		: <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>
	: <math>ws</math> = [[Terrain water storage percentage (Water Overlay)\|Water storage fraction]] of the soil		: <math>ws_{c}</math> = [[Terrain water storage percentage (Water Overlay)\|Water storage fraction]] of the soil
	: <math>\Delta s_{~~x,y~~}</math> = Water flowed in through the bottom boundary from deeper ground layers, in m		: <math>\Delta s_{c}</math> = Water flowed in through the bottom boundary from deeper ground layers, in m

	{{article end		{{article end