Ground flow formula (Water Overlay) - Revision history

Frank@tygron.nl: /* Hydraulic Conductivity with Thickness */

2026-07-10T07:36:49Z

Hydraulic Conductivity with Thickness

← Older revision		Revision as of 07:36, 10 July 2026
Line 39:		Line 39:
	<math>KD = min(KD_{1} , KD_{2} )</math>		<math>KD = min(KD_{1} , KD_{2} )</math>

	<math>V_{KD,t} = \Delta w \cdot KD ~~\cdot~~ \cdot \Delta t</math>		<math>V_{KD,t} = \Delta w \cdot KD \cdot \Delta t</math>

	where:		where:

Frank@tygron.nl: Undo revision 90563 by Frank@tygron.nl (talk)

2026-07-10T07:36:39Z

Undo revision 90563 by Frank@tygron.nl (talk)

← Older revision		Revision as of 07:36, 10 July 2026
Line 39:		Line 39:
	<math>KD = min(KD_{1} , KD_{2} )</math>		<math>KD = min(KD_{1} , KD_{2} )</math>

	<math>V_{KD,t} = ~~\frac{~~\Delta w \cdot KD \cdot ~~\Delta x }{ \Delta x}~~ \cdot \Delta t</math>		<math>V_{KD,t} = \Delta w \cdot KD \cdot \cdot \Delta t</math>

	where:		where:
Line 46:		Line 46:
	: <math>\Delta w</math> = Ground water level difference at time <math>t</math>.		: <math>\Delta w</math> = Ground water level difference at time <math>t</math>.
	: <math>\Delta t</math> = Computational [[Timestep formula (Water Overlay)\|timestep]] in seconds.		: <math>\Delta t</math> = Computational [[Timestep formula (Water Overlay)\|timestep]] in seconds.
	~~: <math>\Delta x</math> = Size of grid cell.~~
	: <math>V_{KD,t}</math> = The amount of water to be transported at time <math>t</math> between one cell and the other.		: <math>V_{KD,t}</math> = The amount of water to be transported at time <math>t</math> between one cell and the other.

Line 52:		Line 51:
	When an [[Aquifer (Water_Overlay)\|aquifer]] is present, its [[Aquifer kd (Water Overlay)\|hydraulic diffusivity]] is used to calculate the water flow.		When an [[Aquifer (Water_Overlay)\|aquifer]] is present, its [[Aquifer kd (Water Overlay)\|hydraulic diffusivity]] is used to calculate the water flow.

	~~Based on conditions being true, the calculated~~ volume of water ~~that is~~ transported through the aquifer is calculated as:		The volume of water transported through the aquifer is calculated as follows:
	: <math>V_{a,t} =		: <math>V_{a,t} =
	\begin{cases}		\begin{cases}
	~~\dfrac{~~ \Delta w_{t} \cdot {KD}_a ~~\cdot \Delta x}{\Delta x}~~ \cdot \Delta t & \text{if } w_{n,t} > z_a \text{ and } KD_a > 0 \\		\Delta w_{t} \cdot {KD}_a \cdot \Delta t & \text{if } w_{n,t} > z_a \text{ and } KD_a > 0 \\
	V_{K(D),t} & \text{otherwise}		V_{K(D),t} & \text{otherwise}
	\end{cases}		\end{cases}
Line 63:		Line 62:
	: <math>\Delta w_{t}</math> = Ground water level difference between the two adjacent cells at time <math>t</math>;		: <math>\Delta w_{t}</math> = Ground water level difference between the two adjacent cells at time <math>t</math>;
	: <math>{KD}_a</math> = The [[Aquifer kd (Water Overlay)\|AQUIFER_KD]] attribute of aquifer.		: <math>{KD}_a</math> = The [[Aquifer kd (Water Overlay)\|AQUIFER_KD]] attribute of aquifer.
	~~: <math>\Delta x</math> = Size of grid cell.~~
	: <math>\Delta t</math> = Computational [[Timestep formula (Water Overlay)\|timestep]] in seconds.		: <math>\Delta t</math> = Computational [[Timestep formula (Water Overlay)\|timestep]] in seconds.
	: <math>w_{n,t}</math> = Ground water level in cell ~~<math>n</math>~~ at time <math>t</math>;		: <math>w_{n,t}</math> = Ground water level in the respective cell at time <math>t</math>;
	: <math>z_a</math> = [[Aquifer datum (Water Overlay)\|the datum height of the aquifer]] at the cell.		: <math>z_a</math> = [[Aquifer datum (Water Overlay)\|the datum height of the aquifer]] at the cell.
	: <math>V_{K(D),t}</math> = The calculated amount of water to be transported at time <math>t</math> between one cell and the other.		: <math>V_{K(D),t}</math> = The calculated amount of water to be transported at time <math>t</math> between one cell and the other.

Frank@tygron.nl at 07:36, 10 July 2026

2026-07-10T07:36:21Z

← Older revision		Revision as of 07:36, 10 July 2026
Line 39:		Line 39:
	<math>KD = min(KD_{1} , KD_{2} )</math>		<math>KD = min(KD_{1} , KD_{2} )</math>

	<math>V_{KD,t} = \Delta w \cdot KD \cdot \cdot \Delta t</math>		<math>V_{KD,t} = \frac{\Delta w \cdot KD \cdot \Delta x }{ \Delta x} \cdot \Delta t</math>

	where:		where:
Line 46:		Line 46:
	: <math>\Delta w</math> = Ground water level difference at time <math>t</math>.		: <math>\Delta w</math> = Ground water level difference at time <math>t</math>.
	: <math>\Delta t</math> = Computational [[Timestep formula (Water Overlay)\|timestep]] in seconds.		: <math>\Delta t</math> = Computational [[Timestep formula (Water Overlay)\|timestep]] in seconds.
			: <math>\Delta x</math> = Size of grid cell.
	: <math>V_{KD,t}</math> = The amount of water to be transported at time <math>t</math> between one cell and the other.		: <math>V_{KD,t}</math> = The amount of water to be transported at time <math>t</math> between one cell and the other.

Line 51:		Line 52:
	When an [[Aquifer (Water_Overlay)\|aquifer]] is present, its [[Aquifer kd (Water Overlay)\|hydraulic diffusivity]] is used to calculate the water flow.		When an [[Aquifer (Water_Overlay)\|aquifer]] is present, its [[Aquifer kd (Water Overlay)\|hydraulic diffusivity]] is used to calculate the water flow.

	~~The~~ volume of water transported through the aquifer is calculated as ~~follows~~:		Based on conditions being true, the calculated volume of water that is transported through the aquifer is calculated as:
	: <math>V_{a,t} =		: <math>V_{a,t} =
	\begin{cases}		\begin{cases}
	\Delta w_{t} \cdot {KD}_a \cdot \Delta t & \text{if } w_{n,t} > z_a \text{ and } KD_a > 0 \\		\dfrac{ \Delta w_{t} \cdot {KD}_a \cdot \Delta x}{\Delta x} \cdot \Delta t & \text{if } w_{n,t} > z_a \text{ and } KD_a > 0 \\
	V_{K(D),t} & \text{otherwise}		V_{K(D),t} & \text{otherwise}
	\end{cases}		\end{cases}
Line 62:		Line 63:
	: <math>\Delta w_{t}</math> = Ground water level difference between the two adjacent cells at time <math>t</math>;		: <math>\Delta w_{t}</math> = Ground water level difference between the two adjacent cells at time <math>t</math>;
	: <math>{KD}_a</math> = The [[Aquifer kd (Water Overlay)\|AQUIFER_KD]] attribute of aquifer.		: <math>{KD}_a</math> = The [[Aquifer kd (Water Overlay)\|AQUIFER_KD]] attribute of aquifer.
			: <math>\Delta x</math> = Size of grid cell.
	: <math>\Delta t</math> = Computational [[Timestep formula (Water Overlay)\|timestep]] in seconds.		: <math>\Delta t</math> = Computational [[Timestep formula (Water Overlay)\|timestep]] in seconds.
	: <math>w_{n,t}</math> = Ground water level in ~~the respective~~ cell at time <math>t</math>;		: <math>w_{n,t}</math> = Ground water level in cell <math>n</math> at time <math>t</math>;
	: <math>z_a</math> = [[Aquifer datum (Water Overlay)\|the datum height of the aquifer]] at the cell.		: <math>z_a</math> = [[Aquifer datum (Water Overlay)\|the datum height of the aquifer]] at the cell.
	: <math>V_{K(D),t}</math> = The calculated amount of water to be transported at time <math>t</math> between one cell and the other.		: <math>V_{K(D),t}</math> = The calculated amount of water to be transported at time <math>t</math> between one cell and the other.

Frank@tygron.nl at 07:22, 10 July 2026

2026-07-10T07:22:20Z

← Older revision		Revision as of 07:22, 10 July 2026
Line 51:		Line 51:
	When an [[Aquifer (Water_Overlay)\|aquifer]] is present, its [[Aquifer kd (Water Overlay)\|hydraulic diffusivity]] is used to calculate the water flow.		When an [[Aquifer (Water_Overlay)\|aquifer]] is present, its [[Aquifer kd (Water Overlay)\|hydraulic diffusivity]] is used to calculate the water flow.

	~~Based on conditions being true, the calculated~~ volume of water ~~that is~~ transported through the aquifer is calculated as:		The volume of water transported through the aquifer is calculated as follows:
	: <math>V_{a,t} =		: <math>V_{a,t} =
	\begin{cases}		\begin{cases}
Line 63:		Line 63:
	: <math>{KD}_a</math> = The [[Aquifer kd (Water Overlay)\|AQUIFER_KD]] attribute of aquifer.		: <math>{KD}_a</math> = The [[Aquifer kd (Water Overlay)\|AQUIFER_KD]] attribute of aquifer.
	: <math>\Delta t</math> = Computational [[Timestep formula (Water Overlay)\|timestep]] in seconds.		: <math>\Delta t</math> = Computational [[Timestep formula (Water Overlay)\|timestep]] in seconds.
	: <math>w_{n,t}</math> = Ground water level in cell ~~<math>n</math>~~ at time <math>t</math>;		: <math>w_{n,t}</math> = Ground water level in the respective cell at time <math>t</math>;
	: <math>z_a</math> = [[Aquifer datum (Water Overlay)\|the datum height of the aquifer]] at the cell.		: <math>z_a</math> = [[Aquifer datum (Water Overlay)\|the datum height of the aquifer]] at the cell.
	: <math>V_{K(D),t}</math> = The calculated amount of water to be transported at time <math>t</math> between one cell and the other.		: <math>V_{K(D),t}</math> = The calculated amount of water to be transported at time <math>t</math> between one cell and the other.

Frank@tygron.nl: /* Hydraulic Conductivity with Thickness */

2026-07-10T07:21:20Z

Hydraulic Conductivity with Thickness

← Older revision		Revision as of 07:21, 10 July 2026
Line 46:		Line 46:
	: <math>\Delta w</math> = Ground water level difference at time <math>t</math>.		: <math>\Delta w</math> = Ground water level difference at time <math>t</math>.
	: <math>\Delta t</math> = Computational [[Timestep formula (Water Overlay)\|timestep]] in seconds.		: <math>\Delta t</math> = Computational [[Timestep formula (Water Overlay)\|timestep]] in seconds.
	~~: <math>\Delta x</math> = Size of grid cell.~~
	: <math>V_{KD,t}</math> = The amount of water to be transported at time <math>t</math> between one cell and the other.		: <math>V_{KD,t}</math> = The amount of water to be transported at time <math>t</math> between one cell and the other.

Frank@tygron.nl: /* Aquifer formula */

2026-07-10T07:21:10Z

Aquifer formula

← Older revision		Revision as of 07:21, 10 July 2026
Line 63:		Line 63:
	: <math>\Delta w_{t}</math> = Ground water level difference between the two adjacent cells at time <math>t</math>;		: <math>\Delta w_{t}</math> = Ground water level difference between the two adjacent cells at time <math>t</math>;
	: <math>{KD}_a</math> = The [[Aquifer kd (Water Overlay)\|AQUIFER_KD]] attribute of aquifer.		: <math>{KD}_a</math> = The [[Aquifer kd (Water Overlay)\|AQUIFER_KD]] attribute of aquifer.
	~~: <math>\Delta x</math> = Size of grid cell.~~
	: <math>\Delta t</math> = Computational [[Timestep formula (Water Overlay)\|timestep]] in seconds.		: <math>\Delta t</math> = Computational [[Timestep formula (Water Overlay)\|timestep]] in seconds.
	: <math>w_{n,t}</math> = Ground water level in cell <math>n</math> at time <math>t</math>;		: <math>w_{n,t}</math> = Ground water level in cell <math>n</math> at time <math>t</math>;

Frank@tygron.nl: /* Hydraulic Conductivity with Thickness */

2026-07-10T07:20:43Z

Hydraulic Conductivity with Thickness

← Older revision		Revision as of 07:20, 10 July 2026
Line 39:		Line 39:
	<math>KD = min(KD_{1} , KD_{2} )</math>		<math>KD = min(KD_{1} , KD_{2} )</math>

	<math>V_{KD,t} = ~~\frac{~~\Delta w \cdot KD \cdot ~~\Delta x }{ \Delta x}~~ \cdot \Delta t</math>		<math>V_{KD,t} = \Delta w \cdot KD \cdot \cdot \Delta t</math>

	where:		where:

Frank@tygron.nl at 07:20, 10 July 2026

2026-07-10T07:20:24Z

← Older revision		Revision as of 07:20, 10 July 2026
Line 55:		Line 55:
	: <math>V_{a,t} =		: <math>V_{a,t} =
	\begin{cases}		\begin{cases}
	\d \Delta w_{t} \cdot {KD}_a \cdot \Delta t & \text{if } w_{n,t} > z_a \text{ and } KD_a > 0 \\		\Delta w_{t} \cdot {KD}_a \cdot \Delta t & \text{if } w_{n,t} > z_a \text{ and } KD_a > 0 \\
	V_{K(D),t} & \text{otherwise}		V_{K(D),t} & \text{otherwise}
	\end{cases}		\end{cases}

Frank@tygron.nl: /* Aquifer formula */

2026-07-10T07:18:52Z

Aquifer formula

← Older revision		Revision as of 07:18, 10 July 2026
Line 55:		Line 55:
	: <math>V_{a,t} =		: <math>V_{a,t} =
	\begin{cases}		\begin{cases}
	\~~dfrac{~~ \Delta w_{t} \cdot {KD}_a ~~\cdot \Delta x}{\Delta x}~~ \cdot \Delta t & \text{if } w_{n,t} > z_a \text{ and } KD_a > 0 \\		\d \Delta w_{t} \cdot {KD}_a \cdot \Delta t & \text{if } w_{n,t} > z_a \text{ and } KD_a > 0 \\
	V_{K(D),t} & \text{otherwise}		V_{K(D),t} & \text{otherwise}
	\end{cases}		\end{cases}

Frank@tygron.nl at 07:17, 10 July 2026

2026-07-10T07:17:01Z

← Older revision		Revision as of 07:17, 10 July 2026
Line 1:		Line 1:
	Ground flow is different from surface flow, since it has to account for the slowdown and porousness of the medium. In general, horizontal ground flow is calculated using formulas described in Harbaugh 2005{{ref\|Harbaugh}}{{ref\|Modflow}}. However, when an [[Aquifer (Water_Overlay)\|aquifer]] is present, the [[ground flow formula (Water Overlay)#Aquifer formula\|Aquifer formula]] is applied.		Ground flow is different from surface flow, since it has to account for the slowdown and porousness of the medium. In general, horizontal ground flow is calculated using formulas described in Harbaugh 2005{{ref\|Harbaugh}}{{ref\|Modflow}}. However, when an [[Aquifer (Water_Overlay)\|aquifer]] is present, the [[ground flow formula (Water Overlay)#Aquifer formula\|Aquifer formula]] is applied.

	It depends on the ~~configuration~~ of the [[Hydraulic conductivity with thickness (Water Overlay)\|HYDRAULIC_CONDUCTIVITY_WITH_THICKNESS]] attribute ~~value~~ in the [[Water Overlay]] ~~what Hydraulic Conductivity formula is used~~:		The Hydraulic Conductivity formula used depends on the value of the [[Hydraulic conductivity with thickness (Water Overlay)\|HYDRAULIC_CONDUCTIVITY_WITH_THICKNESS]] attribute in the [[Water Overlay]]:
	* A value <math><= 0</math> means [[Ground flow formula (Water Overlay)#Hydraulic Conductivity without Thickness\|Hydraulic Conductivity without Thickness]] formula will be used.		* A value <math><= 0</math> means [[Ground flow formula (Water Overlay)#Hydraulic Conductivity without Thickness\|Hydraulic Conductivity without Thickness]] formula will be used.
	* A value <math>> 0</math> means [[Ground flow formula (Water Overlay)#Hydraulic Conductivity with Thickness\|Hydraulic Conductivity with Thickness]] formula will be used.		* A value <math>> 0</math> means [[Ground flow formula (Water Overlay)#Hydraulic Conductivity with Thickness\|Hydraulic Conductivity with Thickness]] formula will be used.

← Older revision		Revision as of 07:17, 10 July 2026
Line 1:		Line 1:
	Ground flow is different from surface flow, since it has to account for the slowdown and porousness of the medium. In general, horizontal ground flow is calculated using formulas described in Harbaugh 2005{{ref\|Harbaugh}}{{ref\|Modflow}}. However, when an [[Aquifer (Water_Overlay)\|aquifer]] is present, the [[ground flow formula (Water Overlay)#Aquifer formula\|Aquifer formula]] is applied.		Ground flow is different from surface flow, since it has to account for the slowdown and porousness of the medium. In general, horizontal ground flow is calculated using formulas described in Harbaugh 2005{{ref\|Harbaugh}}{{ref\|Modflow}}. However, when an [[Aquifer (Water_Overlay)\|aquifer]] is present, the [[ground flow formula (Water Overlay)#Aquifer formula\|Aquifer formula]] is applied.

	It depends on the ~~configuration~~ of the [[Hydraulic conductivity with thickness (Water Overlay)\|HYDRAULIC_CONDUCTIVITY_WITH_THICKNESS]] attribute ~~value~~ in the [[Water Overlay]] ~~what Hydraulic Conductivity formula is used~~:		The Hydraulic Conductivity formula used depends on the value of the [[Hydraulic conductivity with thickness (Water Overlay)\|HYDRAULIC_CONDUCTIVITY_WITH_THICKNESS]] attribute in the [[Water Overlay]]:
	* A value <math><= 0</math> means [[Ground flow formula (Water Overlay)#Hydraulic Conductivity without Thickness\|Hydraulic Conductivity without Thickness]] formula will be used.		* A value <math><= 0</math> means [[Ground flow formula (Water Overlay)#Hydraulic Conductivity without Thickness\|Hydraulic Conductivity without Thickness]] formula will be used.
	* A value <math>> 0</math> means [[Ground flow formula (Water Overlay)#Hydraulic Conductivity with Thickness\|Hydraulic Conductivity with Thickness]] formula will be used.		* A value <math>> 0</math> means [[Ground flow formula (Water Overlay)#Hydraulic Conductivity with Thickness\|Hydraulic Conductivity with Thickness]] formula will be used.