Ground water depth formula (Subsidence Overlay) - Revision history

Maxim@tygron.com at 08:01, 9 October 2025

2025-10-09T08:01:43Z

← Older revision		Revision as of 08:01, 9 October 2025
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			{{deprecated}}
	At the start of a simulation, the ground water depth is initialized with the [[Ground water GeoTIFF (Subsidence Overlay)\|ground water depth GeoTIFF]] (if provided) and is optionally overwritten by (managed) water areas' water level.		At the start of a simulation, the ground water depth is initialized with the [[Ground water GeoTIFF (Subsidence Overlay)\|ground water depth GeoTIFF]] (if provided) and is optionally overwritten by (managed) water areas' water level.

Frank@tygron.nl at 12:25, 17 January 2022

2022-01-17T12:25:13Z

← Older revision		Revision as of 12:25, 17 January 2022
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	At the start of a simulation, the ground water depth is initialized with the [[Ground water ~~geotiff~~ (Subsidence Overlay)\|ground water depth ~~geotiff~~]] (if provided) and is optionally overwritten by (managed) water areas' water level.		At the start of a simulation, the ground water depth is initialized with the [[Ground water GeoTIFF (Subsidence Overlay)\|ground water depth GeoTIFF]] (if provided) and is optionally overwritten by (managed) water areas' water level.

	Furthermore, the ground water level can be managed with [[Drainage feature (Subsidence Overlay)\|drainages]] (provided as underground buildings), either [[Drainage (Subsidence Overlay)\|actively]] or [[Low passive_drainage (Subsidence Overlay)\|passively]].		Furthermore, the ground water level can be managed with [[Drainage feature (Subsidence Overlay)\|drainages]] (provided as underground buildings), either [[Drainage (Subsidence Overlay)\|actively]] or [[Low passive_drainage (Subsidence Overlay)\|passively]].

Frank@tygron.nl at 06:57, 28 May 2021

2021-05-28T06:57:27Z

Frank@tygron.nl: /* Inundation */

2021-03-15T17:01:17Z

Inundation

← Older revision		Revision as of 17:01, 15 March 2021
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	\begin{cases}		\begin{cases}
	d_{gw,y} =		d_{gw,y} =
	0, & \text{if } d_{a} + \Delta{d_{~~gw,y~~}} < 0 \\		0, & \text{if } d_{a} + \Delta{d_{inc}} < 0 \\
	d_{gw,y}, & \text{otherwise} \\		d_{gw,y}, & \text{otherwise} \\
	\end{cases}		\end{cases}
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	: <math>d_{a} </math> is the current relative water depth of water level area a.		: <math>d_{a} </math> is the current relative water depth of water level area a.
	: <math>d_{gw,y}</math> is the calculated adjusted ground water depth for year y, based on the occurred subsidence and indexation of previous years.		: <math>d_{gw,y}</math> is the calculated adjusted ground water depth for year y, based on the occurred subsidence and indexation of previous years.
	: <math>\Delta{d_{~~gw,y~~}}</math> is the estimated change of the ground water level based on occurred subsidence and indexation.		: <math>\Delta{d_{inc}}</math> is the estimated change of the ground water level based on occurred subsidence and indexation, described in the previous section.

	====Ground Water change examples====		====Ground Water change examples====

Frank@tygron.nl: /* Inundation */

2021-03-15T16:34:32Z

Inundation

← Older revision		Revision as of 16:34, 15 March 2021
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	\begin{cases}		\begin{cases}
	d_{gw,y} =		d_{gw,y} =
	0, & \text{if } d_{a} + \Delta{d_{~~inc~~}} < 0 \\		0, & \text{if } d_{a} + \Delta{d_{gw,y}} < 0 \\
	d_{gw,y}, & \text{otherwise} \\		d_{gw,y}, & \text{otherwise} \\
	\end{cases}		\end{cases}
	</math>		</math>

			: <math>d_{a} </math> is the current relative water depth of water level area a.
			: <math>d_{gw,y}</math> is the calculated adjusted ground water depth for year y, based on the occurred subsidence and indexation of previous years.
			: <math>\Delta{d_{gw,y}}</math> is the estimated change of the ground water level based on occurred subsidence and indexation.

	====Ground Water change examples====		====Ground Water change examples====

Frank@tygron.nl: /* Ground water level managed by water level areas */

2021-03-15T16:15:28Z

Ground water level managed by water level areas

← Older revision		Revision as of 16:15, 15 March 2021
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	: <math>d_{gw,y}</math> is the calculated adjusted ground water depth for year y, based on the occurred subsidence and indexation of previous years.		: <math>d_{gw,y}</math> is the calculated adjusted ground water depth for year y, based on the occurred subsidence and indexation of previous years.
	: <math>d_{gw,0}</math> is the initial ground water depth at the start of the simulation.		: <math>d_{gw,0}</math> is the initial ground water depth at the start of the simulation.
	: <math>\Delta{d_{gw,y}}</math> is the estimated change of the ground water level based on occurred subsidence and indexation.		: <math>\Delta{d_{gw,y}}</math> is the estimated change of the ground water level based on occurred subsidence and indexation.<noinclude>

	====Inundation====		====Inundation====

Frank@tygron.nl: /* Ground water level managed by water level areas */

2021-03-15T16:14:49Z

Ground water level managed by water level areas

← Older revision		Revision as of 16:14, 15 March 2021
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	: <math>d_{gw,y}</math> is the calculated adjusted ground water depth for year y, based on the occurred subsidence and indexation of previous years.		: <math>d_{gw,y}</math> is the calculated adjusted ground water depth for year y, based on the occurred subsidence and indexation of previous years.
	: <math>d_{gw,0}</math> is the initial ground water depth at the start of the simulation.		: <math>d_{gw,0}</math> is the initial ground water depth at the start of the simulation.
	: <math>\Delta{d_{gw,y}}</math> is the estimated change of the ground water level based on occurred subsidence and indexation.~~<noinclude>~~		: <math>\Delta{d_{gw,y}}</math> is the estimated change of the ground water level based on occurred subsidence and indexation.

	====Inundation====		====Inundation====

Frank@tygron.nl: /* Inundation */

2021-03-15T15:57:56Z

Inundation

← Older revision		Revision as of 15:57, 15 March 2021
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	In case this option is turned on, the following case is handled before drainage and ground water depth adjustments are considered.		In case this option is turned on, the following case is handled before drainage and ground water depth adjustments are considered.

	<math>		<math>
	\begin{cases}		\begin{cases}

Frank@tygron.nl at 15:57, 15 March 2021

2021-03-15T15:57:41Z

← Older revision		Revision as of 15:57, 15 March 2021
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	<math>\Delta{d_{gw,y}} = \Delta{d_{low}}+\Delta{d_{mid}}+\Delta{d_{high}}</math>		<math>\Delta{d_{gw,y}} = \Delta{d_{low}}+\Delta{d_{mid}}+\Delta{d_{high}}</math>

	<math>d_{gw,y} = max(0.0, d_{gw} + \Delta{d_{gw,y}})</math>		<math>d_{gw,y} = max(0.0, d_{gw,0} + \Delta{d_{gw,y}})</math>

	where		where
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	: <math>s_{y-1}</math> is the subsidence that occurred up to year y.		: <math>s_{y-1}</math> is the subsidence that occurred up to year y.
	: <math>d_{gw,y}</math> is the calculated adjusted ground water depth for year y, based on the occurred subsidence and indexation of previous years.		: <math>d_{gw,y}</math> is the calculated adjusted ground water depth for year y, based on the occurred subsidence and indexation of previous years.
	: <math>d_{gw}</math> is the initial ground water depth at the start of the simulation.		: <math>d_{gw,0}</math> is the initial ground water depth at the start of the simulation.
	: <math>\Delta{d_{gw,y}}</math> is the estimated change of the ground water level based on occurred subsidence and indexation.<noinclude>		: <math>\Delta{d_{gw,y}}</math> is the estimated change of the ground water level based on occurred subsidence and indexation.<noinclude>

			====Inundation====
			Initially, or due to subsidence, the surface height of a cell can be lower than the configured water level. In such case, for certain situations, it can be said that the cell is therefore inundated by water from the nearby waterway. When inundated, the cell's ground water level will most certainly raise to the surface level.
			This option is can be turned on and off using the subsidence overlay model attribute [[Inundate land below water level (Subsidence Overlay)\|Inundate land below water level]].

			In case this option is turned on, the following case is handled before drainage and ground water depth adjustments are considered.
			<math>
			\begin{cases}
			d_{gw,y} =
			0, & \text{if } d_{a} + \Delta{d_{inc}} < 0 \\
			d_{gw,y}, & \text{otherwise} \\
			\end{cases}
			</math>

	====Ground Water change examples====		====Ground Water change examples====

Frank@tygron.nl: /* Ground water level managed by water level areas */

2021-02-18T12:00:58Z

Ground water level managed by water level areas

← Older revision		Revision as of 12:00, 18 February 2021
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	Next, based on the old and new depths, the ground water depth change is divided into three sections, each which its own rate of contribution.		Next, based on the old and new depths, the ground water depth change is divided into three sections, each which its own rate of contribution.

	<math>\Delta{d_{low}} = 0.6 \cdot ~~(\max(0.0,~~ min(0.6, d_{a,adj})- ~~max(0.0,~~ min(0.6, d_{a}))</math>		<math>\Delta{d_{low}} = 0.6 \cdot min(0.6, d_{a,adj})- min(0.6, d_{a})</math>

	<math>\Delta{d_{mid}} = \frac{\max(0.6, min(1.0, d_{a,adj}))+ max(0.6, min(1.0, d_{a}))}{2.0} \cdot (\max(0.6, min(1.0, d_{a,adj}))- max(0.6, min(1.0, d_{a})))</math>		<math>\Delta{d_{mid}} = \frac{\max(0.6, min(1.0, d_{a,adj}))+ max(0.6, min(1.0, d_{a}))}{2.0} \cdot (\max(0.6, min(1.0, d_{a,adj}))- max(0.6, min(1.0, d_{a})))</math>

← Older revision		Revision as of 06:57, 28 May 2021
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	At the start of a simulation, the ground water depth is initialized with the [[Ground water geotiff (Subsidence Overlay)\|ground water depth geotiff]] (if provided) and is optionally overwritten by (managed) water ~~level~~ areas' water level.		At the start of a simulation, the ground water depth is initialized with the [[Ground water geotiff (Subsidence Overlay)\|ground water depth geotiff]] (if provided) and is optionally overwritten by (managed) water areas' water level.

	Furthermore, the ground water level can be managed with [[Drainage feature (Subsidence Overlay)\|drainages]] (provided as underground buildings), either [[Drainage (Subsidence Overlay)\|actively]] or [[Low passive_drainage (Subsidence Overlay)\|passively]].		Furthermore, the ground water level can be managed with [[Drainage feature (Subsidence Overlay)\|drainages]] (provided as underground buildings), either [[Drainage (Subsidence Overlay)\|actively]] or [[Low passive_drainage (Subsidence Overlay)\|passively]].

	Additionally the terrain height can change due to subsidence that occurred in previous years and due to actions taken that raised the terrain. Managed water ~~level~~ areas can react to these changes when indexation is configured. For indexation, see [[Indexation formula (Subsidence Overlay)\|indexation formula]].		Additionally the terrain height can change due to subsidence that occurred in previous years and due to actions taken that raised the terrain. Managed water areas can react to these changes when indexation is configured. For indexation, see [[Indexation formula (Subsidence Overlay)\|indexation formula]].

	The [[Ground water depth formula (Subsidence Overlay)\|following formulas]] describe how the yearly adjusted ground water depths are obtained.		The [[Ground water depth formula (Subsidence Overlay)\|following formulas]] describe how the yearly adjusted ground water depths are obtained.
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	: <math>d_{gw,y}</math> is the calculated ground water depth of a grid cell at year y.		: <math>d_{gw,y}</math> is the calculated ground water depth of a grid cell at year y.
	: <math>d_{d,active}</math> is the ground water depth actively maintained by a drainage		: <math>d_{d,active}</math> is the ground water depth actively maintained by a drainage
	: <math>d_{a}</math> is the ground water depth of the managed water ~~level~~ area.		: <math>d_{a}</math> is the ground water depth of the managed water area.
	: <math>\Delta{d_{a,y}}</math> is the area water level adjustment for year y.		: <math>\Delta{d_{a,y}}</math> is the area water level adjustment for year y.
	: <math>d_{d, passive}</math> is the ground water level passively maintained by drainages.		: <math>d_{d, passive}</math> is the ground water level passively maintained by drainages.
	: <math>\Delta{d_{a,s,y}}</math> is the [[#Ground water level managed by water ~~level~~ areas\|ground water level increase]] calculated based on the are water level adjustment due to indexation and the subsidence in the previous year.		: <math>\Delta{d_{a,s,y}}</math> is the [[#Ground water level managed by water areas\|ground water level increase]] calculated based on the are water level adjustment due to indexation and the subsidence in the previous year.

	====Ground water level managed by water ~~level~~ areas====		====Ground water level managed by water areas====
	[[File:ground-water-graph.jpg\|400px\|thumb\|right\|The effect of changes of managed surface water levels (by water ~~level~~ areas) on the ground water level. The x-axis indicates the relative depth of the managed surface water level. The y-axis indicates the meters of change to the ground water level, per meter change in surface water level. The smaller the relative depth is, the less the ground water level equalizes with changes in the managed surface water level.]]		[[File:ground-water-graph.jpg\|400px\|thumb\|right\|The effect of changes of managed surface water levels (by water areas) on the ground water level. The x-axis indicates the relative depth of the managed surface water level. The y-axis indicates the meters of change to the ground water level, per meter change in surface water level. The smaller the relative depth is, the less the ground water level equalizes with changes in the managed surface water level.]]
	The ground water level can also be managed by water ~~level~~ areas, which control the surface water levels. To make sure ground water levels do not rise (too much), surface water levels in the water ~~level~~ areas can be lowered automatically with respect to the subsidence. This process is called indexation. The new ground water level can then be estimated based on the indexation on the managed water level of surface water and the calculated subsidence of the previous year. The increment in ground water level is rarely exactly the adjustment of the managed surface water level and is often less, depending on the relative depth of the surface water level. The following formulas have been developed to estimate the increase of the ground water level.		The ground water level can also be managed by water areas, which control the surface water levels. To make sure ground water levels do not rise (too much), surface water levels in the water areas can be lowered automatically with respect to the subsidence. This process is called indexation. The new ground water level can then be estimated based on the indexation on the managed water level of surface water and the calculated subsidence of the previous year. The increment in ground water level is rarely exactly the adjustment of the managed surface water level and is often less, depending on the relative depth of the surface water level. The following formulas have been developed to estimate the increase of the ground water level.

	The new relative surface water level depth is calculated as:		The new relative surface water level depth is calculated as:
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	where		where
	: <math>d_{a} </math> is the current relative water depth of water ~~level~~ area a.		: <math>d_{a} </math> is the current relative water depth of water area a.
	: <math>d_{a,adj}</math> is the adjusted relative water depth of water ~~level~~ area a.		: <math>d_{a,adj}</math> is the adjusted relative water depth of water area a.
	: <math>\Delta{d_{a,y-1}}></math> is the water level adjustment for indexation of current year y.		: <math>\Delta{d_{a,y-1}}></math> is the water level adjustment for indexation of current year y.
	: <math>s_{y-1}</math> is the subsidence that occurred up to year y.		: <math>s_{y-1}</math> is the subsidence that occurred up to year y.
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	</math>		</math>

	: <math>d_{a} </math> is the current relative water depth of water ~~level~~ area a.		: <math>d_{a} </math> is the current relative water depth of water area a.
	: <math>d_{gw,y}</math> is the calculated adjusted ground water depth for year y, based on the occurred subsidence and indexation of previous years.		: <math>d_{gw,y}</math> is the calculated adjusted ground water depth for year y, based on the occurred subsidence and indexation of previous years.
	: <math>\Delta{d_{inc}}</math> is the estimated change of the ground water level based on occurred subsidence and indexation, described in the previous section.		: <math>\Delta{d_{inc}}</math> is the estimated change of the ground water level based on occurred subsidence and indexation, described in the previous section.