Surface model (Water Overlay) - Revision history

Maxim@tygron.com at 12:45, 8 July 2026

2026-07-08T12:45:12Z

← Older revision		Revision as of 12:45, 8 July 2026
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	General sequence of computational steps:		General sequence of computational steps:
	# ~~Each cell's~~ elevation ~~value~~ (B in Fig. 3) is ~~set equal to~~ the ~~value at its center and the interface midpoints~~.		# The bottom elevation (B in Fig. 3) is reconstructed using a piecewise linear approximation across the cell.
	# Slopes of conserved variables are reconstructed (continuity and momentum in ''x''- and ''y''-direction).		# Slopes of conserved variables are reconstructed (continuity and momentum in ''x''- and ''y''-direction).
	# Values of conserved variables at the cell interface midpoints are compared with the left-sided and right-sided values with respect to the cell's center.		# Values of conserved variables at the cell interface midpoints are compared with the left-sided and right-sided values with respect to the cell's center.
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	For all [[Terrain water (Water Overlay)\|water terrains]] in a water area, the water level is set to the [[Water level (Water Overlay)\|WATER_LEVEL]] attribute of the corresponding [[Water area (Water Overlay)\|water area]].		For all [[Terrain water (Water Overlay)\|water terrains]] in a water area, the water level is set to the [[Water level (Water Overlay)\|WATER_LEVEL]] attribute of the corresponding [[Water area (Water Overlay)\|water area]].

	In contrast to water areas, which generate water on water terrains, inundation areas generate water over all grid cells, regardless of its terrain type. Similarly, the ~~volume of~~ water per grid cell is determined by the [[Inundation level (Water Overlay)\|INUNDATION_LEVEL]] attribute as provided by the corresponding inundation area.		In contrast to water areas, which generate water on water terrains, inundation areas generate water over all grid cells, regardless of its terrain type. Similarly, the water level per grid cell is determined by the [[Inundation level (Water Overlay)\|INUNDATION_LEVEL]] attribute as provided by the corresponding inundation area.

	If a grid cell is neither part of any water area nor inundation area, or the assigned water level is lower than its [[Elevation model (Water Overlay)\|bottom elevation]], the water depth is assumed to be zero and the water level becomes equal to the bottom elevation. In turn, this bottom (or surface) elevation is equal to the [[elevation model]], though it may be altered by the presence of a building or the [[Breach height (Water Overlay)\|BREACH_HEIGHT]] attribute of a [[Breach (Water Overlay)\|breach]].		If a grid cell is neither part of any water area nor inundation area, or the assigned water level is lower than its [[Elevation model (Water Overlay)\|bottom elevation]], the water depth is assumed to be zero and the water level becomes equal to the bottom elevation. In turn, this bottom (or surface) elevation is equal to the [[elevation model]], though it may be altered by the presence of a building or the [[Breach height (Water Overlay)\|BREACH_HEIGHT]] attribute of a [[Breach (Water Overlay)\|breach]].

Frank@tygron.nl at 12:06, 7 July 2026

2026-07-07T12:06:32Z

← Older revision		Revision as of 12:06, 7 July 2026
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	===Water level initialization===		===Water level initialization===
	In theory, each grid cell can have a unique bottom elevation and accompanying water depth, yielding a certain water surface elevation (or water level). ~~However, in~~ practice, water levels are often initialized for ~~large~~ groups of cells ~~rather than individual cells, assuming that each (water level) area in a project has been assigned a~~ [[water level (Water Overlay)\|water level]]. During the initialization phase a distinction is made between two types:		In theory, each grid cell can have a unique bottom elevation and accompanying water depth, yielding a certain water surface elevation (or water level). In practice, water levels are often initialized for groups of cells based on the [[water level (Water Overlay)\|water level]] assigned to each area. During the initialization phase a distinction is made between two types:
	* [[water level (Water Overlay)\|Water level]]s of [[Water area (Water Overlay)\|water areas]];		* [[water level (Water Overlay)\|Water level]]s of [[Water area (Water Overlay)\|water areas]];
	* [[inundation level (Water Overlay)\|Inundation level]]s of [[Inundation area (Water Overlay)\|inundation areas]].		* [[inundation level (Water Overlay)\|Inundation level]]s of [[Inundation area (Water Overlay)\|inundation areas]].

	For all [[Terrain water (Water Overlay)\|water ~~terrain~~]]s in a water area, the ~~volume of~~ water ~~per grid cell~~ is ~~such that the resulting water level at those locations conforms the value of~~ the [[Water level (Water Overlay)\|WATER_LEVEL]] attribute ~~as provided by~~ the corresponding [[Water area (Water Overlay)\|water area]].		For all [[Terrain water (Water Overlay)\|water terrains]] in a water area, the water level is set to the [[Water level (Water Overlay)\|WATER_LEVEL]] attribute of the corresponding [[Water area (Water Overlay)\|water area]].

	In contrast to water areas, which generate water on water terrains, inundation areas generate water over all grid cells, regardless of its terrain type. Similarly, the volume of water per grid cell is determined by the [[Inundation level (Water Overlay)\|INUNDATION_LEVEL]] attribute as provided by the corresponding inundation area.		In contrast to water areas, which generate water on water terrains, inundation areas generate water over all grid cells, regardless of its terrain type. Similarly, the volume of water per grid cell is determined by the [[Inundation level (Water Overlay)\|INUNDATION_LEVEL]] attribute as provided by the corresponding inundation area.

Frank@tygron.nl at 09:06, 6 July 2026

2026-07-06T09:06:14Z

← Older revision		Revision as of 09:06, 6 July 2026
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	\|}		\|}

	This scheme deviates from the original Saint-Venant equations in that it approaches the system in terms of water surface elevation (''w = h + B'') and flux (''hu'' and ''hv''), instead of just the water depth (''h''). The conceptual image in Fig. 1 aims to clarify on the various terms in the model equations. This method relies on a continuous piecewise linear approximation of the surface, which is further explained on [[Elevation model (Water Overlay)\|this]] page.		This scheme deviates from the original Saint-Venant equations in that it approaches the system in terms of water surface elevation (''w = h + B'') and flux (''hu'' and ''hv''), instead of just the water depth (''h''). The conceptual image in Fig. 1 aims to clarify the various terms in the model equations. This method relies on a continuous piecewise linear approximation of the surface, which is further explained on [[Elevation model (Water Overlay)\|this]] page.

	====Shoreline reconstruction====		====Shoreline reconstruction====
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	In contrast to water areas, which generate water on water terrains, inundation areas generate water over all grid cells, regardless of its terrain type. Similarly, the volume of water per grid cell is determined by the [[Inundation level (Water Overlay)\|INUNDATION_LEVEL]] attribute as provided by the corresponding inundation area.		In contrast to water areas, which generate water on water terrains, inundation areas generate water over all grid cells, regardless of its terrain type. Similarly, the volume of water per grid cell is determined by the [[Inundation level (Water Overlay)\|INUNDATION_LEVEL]] attribute as provided by the corresponding inundation area.

	If a grid cell is neither part of any water area nor inundation area, or the assigned water level is lower than its [[~~terrain height~~ (Water Overlay)\|bottom elevation]], the water depth is assumed to be zero and the water level becomes equal to the bottom elevation. In turn, this bottom (or surface) elevation is equal to the [[elevation model]], though it may be altered by the presence of a building or the [[Breach height (Water Overlay)\|BREACH_HEIGHT]] attribute of a [[Breach (Water Overlay)\|breach]].		If a grid cell is neither part of any water area nor inundation area, or the assigned water level is lower than its [[Elevation model (Water Overlay)\|bottom elevation]], the water depth is assumed to be zero and the water level becomes equal to the bottom elevation. In turn, this bottom (or surface) elevation is equal to the [[elevation model]], though it may be altered by the presence of a building or the [[Breach height (Water Overlay)\|BREACH_HEIGHT]] attribute of a [[Breach (Water Overlay)\|breach]].

	===Water velocity initialization===		===Water velocity initialization===
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	* In the case of [[Ground model (Water Overlay)\|subsurface flow]] a different flow system with different equations are used.		* In the case of [[Ground model (Water Overlay)\|subsurface flow]] a different flow system with different equations are used.
	* In addition to water flowing in between grid cells, water can also flow ''through'' [[Hydraulic structures (Water Overlay)\|hydraulic buildings]].		* In addition to water flowing in between grid cells, water can also flow ''through'' [[Hydraulic structures (Water Overlay)\|hydraulic buildings]].
	* The [[Design flood elevation m ~~model attribute~~ (Water Overlay)\|DESIGN_FLOOD_ELEVATION_M]] attribute confines the maximum surface elevation induced by buildings.		* The [[Design flood elevation m (Water Overlay)\|DESIGN_FLOOD_ELEVATION_M]] attribute confines the maximum surface elevation induced by buildings.
	\|references=		\|references=
	<references>		<references>

Frank@tygron.nl at 08:56, 6 July 2026

2026-07-06T08:56:48Z

← Older revision		Revision as of 08:56, 6 July 2026
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	\begin{align}		\begin{align}
	\frac{\partial h}{\partial t} &+ \frac{\partial (hu)}{\partial x} + \frac{\partial (hv)}{\partial y} = 0,\\[3pt]		\frac{\partial h}{\partial t} &+ \frac{\partial (hu)}{\partial x} + \frac{\partial (hv)}{\partial y} = 0,\\[3pt]
	\frac{\partial (hu)}{\partial t} &+ \frac{\partial}{\partial x} \left( hu^2 + \frac{1}{2} gh^2 \right) + \frac{\partial (huv)}{\partial y} = -gh \frac{\partial B}{\partial x} - ghn^2u \sqrt{u^2 + v^2} h^{-\frac{4}{3}},\\[3pt]		\frac{\partial (hu)}{\partial t} &+ \frac{\partial}{\partial x} \left( hu^2 + \frac{1}{2} gh^2 \right) + \frac{\partial (huv)}{\partial y} = -gh \frac{\partial B}{\partial x} - ghn^2u \sqrt{u^2 + v^2} h^{-\frac{4}{3}} ,\\[3pt]
	\frac{\partial (hv)}{\partial t} &+ \frac{\partial (huv)}{\partial x} + \frac{\partial}{\partial y} \left( hv^2 + \frac{1}{2} gh^2 \right) = -gh \frac{\partial B}{\partial y} - ghn^2v \sqrt{u^2 + v^2} h^{-\frac{4}{3}},		\frac{\partial (hv)}{\partial t} &+ \frac{\partial (huv)}{\partial x} + \frac{\partial}{\partial y} \left( hv^2 + \frac{1}{2} gh^2 \right) = -gh \frac{\partial B}{\partial y} - ghn^2v \sqrt{u^2 + v^2} h^{-\frac{4}{3}} ,
	\end{align}		\end{align}
	</math>		</math>

Rudolf@tygron.nl: /* Microrelief and minimum flow threshold */

2026-02-25T13:19:38Z

Microrelief and minimum flow threshold

← Older revision		Revision as of 13:19, 25 February 2026
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	\|page=		\|page=
	\|source=		\|source=
	\|link=https://www.tuwien.at/index.php?eID=dumpFile&t=f&f=150915&token=e51c85712b7e70bcb769575d03f4680753d55f01~~, http://visdom.at/media/pdf/publications/Poster.pdf~~		\|link=https://www.tuwien.at/index.php?eID=dumpFile&t=f&f=150915&token=e51c85712b7e70bcb769575d03f4680753d55f01
	\|lastvisit=2026-02-25		\|lastvisit=2026-02-25
	}}		}}

Rudolf@tygron.nl at 11:23, 25 February 2026

2026-02-25T11:23:27Z

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	\|page=		\|page=
	\|source=		\|source=
	\|link=~~http~~://~~www.math~~.tamu.edu/~gpetrova/KPSV.pdf		\|link=https://people.tamu.edu/~gpetrova//KPSV.pdf
	\|lastvisit=~~2019~~-04-11		\|lastvisit=2026-02-25
	}}		}}
	</references>		</references>

Rudolf@tygron.nl at 11:19, 25 February 2026

2026-02-25T11:19:00Z

← Older revision		Revision as of 11:19, 25 February 2026
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	\|source=		\|source=
	\|link=https://www.tuwien.at/index.php?eID=dumpFile&t=f&f=150915&token=e51c85712b7e70bcb769575d03f4680753d55f01, http://visdom.at/media/pdf/publications/Poster.pdf		\|link=https://www.tuwien.at/index.php?eID=dumpFile&t=f&f=150915&token=e51c85712b7e70bcb769575d03f4680753d55f01, http://visdom.at/media/pdf/publications/Poster.pdf
	\|lastvisit=~~2015~~-02-25		\|lastvisit=2026-02-25
	}}		}}
	{{ref\|Kurganov2		{{ref\|Kurganov2

Rudolf@tygron.nl at 11:18, 25 February 2026

2026-02-25T11:18:16Z

← Older revision		Revision as of 11:18, 25 February 2026
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	\|page=		\|page=
	\|source=		\|source=
	\|link=~~http~~://~~citeseerx~~.~~ist~~.~~psu~~.~~edu/viewdoc/download~~?~~doi~~=~~10.1.1.700.7977~~&~~rep~~=~~rep1~~&~~type~~=~~pdf~~, http://visdom.at/media/pdf/publications/Poster.pdf		\|link=https://www.tuwien.at/index.php?eID=dumpFile&t=f&f=150915&token=e51c85712b7e70bcb769575d03f4680753d55f01, http://visdom.at/media/pdf/publications/Poster.pdf
	\|lastvisit=~~2018~~-06-29		\|lastvisit=2015-02-25
	}}		}}
	{{ref\|Kurganov2		{{ref\|Kurganov2

Rudolf@tygron.nl at 14:39, 17 October 2025

2025-10-17T14:39:34Z

← Older revision		Revision as of 14:39, 17 October 2025
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	__NOTOC__		__NOTOC__
	[[File:Waterlevel_schematic.png\|300px\|thumb\|right\|Fig. 1. For each grid cell:<br>''B'' = bottom elevation<br>''h'' = water depth<br>''w'' = water surface elevation]]		[[File:Waterlevel_schematic.png\|300px\|thumb\|right\|Fig. 1. For each grid cell:<br>''B'' = bottom elevation<br>''h'' = water depth<br>''w'' = water surface elevation]]
	[[File:Inundation overlay 04 HWP(1).PNG\|thumb\|250px\|Fig. 2. A 2-D grid-based representation of average water depths, discharges and bathymetry in a case where the middle cell is fully flooded in the y-dimension, but only partially flooded in the x-dimension. Blue solid and red dashed lines denote the waterlines and bathymetry slopes in both dimensions, respectively. For a bilinear reconstruction, the cell averages coincide with the values at the cell centers, while bathymetry is approximated by its values at the cell vertices.<ref ~~name="~~Horvath~~"/>~~]]		[[File:Inundation overlay 04 HWP(1).PNG\|thumb\|250px\|Fig. 2. A 2-D grid-based representation of average water depths, discharges and bathymetry in a case where the middle cell is fully flooded in the y-dimension, but only partially flooded in the x-dimension. Blue solid and red dashed lines denote the waterlines and bathymetry slopes in both dimensions, respectively. For a bilinear reconstruction, the cell averages coincide with the values at the cell centers, while bathymetry is approximated by its values at the cell vertices.{{ref\|Horvath}}]]
	[[File:Inundation overlay 04 HWP(2).PNG\|thumb\|250px\|Fig. 3. Continuous bathymetry function (green line) and its piecewise linear approximation (brown dots). The approximated function values equal to the continuous ones at the cell vertices (green dots). The cell average value (blue dot) equals both the average value of the vertex values (green dots) and the average value of the values at the cell interface midpoints (brown dots).<ref ~~name="~~Horvath~~"/>~~]]		[[File:Inundation overlay 04 HWP(2).PNG\|thumb\|250px\|Fig. 3. Continuous bathymetry function (green line) and its piecewise linear approximation (brown dots). The approximated function values equal to the continuous ones at the cell vertices (green dots). The cell average value (blue dot) equals both the average value of the vertex values (green dots) and the average value of the values at the cell interface midpoints (brown dots).{{ref\|Horvath}}]]
	The [[Water Module]]'s primary function is simulating two-dimensional flow of water across the surface. In order to do this, the project area is first discretized into ''x'' by ''y'' cells depending on the configured [[grid cell size]]. Secondly, water is initialized in the model. Finally, a set of rules is required that describes the behavior of the flow.		The [[Water Module]]'s primary function is simulating two-dimensional flow of water across the surface. In order to do this, the project area is first discretized into ''x'' by ''y'' cells depending on the configured [[grid cell size]]. Secondly, water is initialized in the model. Finally, a set of rules is required that describes the behavior of the flow.

	===Surface flow scheme===		===Surface flow scheme===
	In the model, imbalances in the water surface elevation across the grid drive the flow of water until a state of equilibrium is reached in terms of ''h'' and flux. Behavior of the flow is described by a second-order semi-discrete central-upwind scheme produced by Kurganov and Petrova (2007)<ref ~~name="~~Kurganov2~~"/>~~, which is based on the 2-D Saint-Venant equations (a.k.a. shallow water equations):		In the model, imbalances in the water surface elevation across the grid drive the flow of water until a state of equilibrium is reached in terms of ''h'' and flux. Behavior of the flow is described by a second-order semi-discrete central-upwind scheme produced by Kurganov and Petrova (2007){{ref\|Kurganov2}}, which is based on the 2-D Saint-Venant equations (a.k.a. shallow water equations):

	:<math>		:<math>
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	====Shoreline reconstruction====		====Shoreline reconstruction====
	This scheme is further extended with the shoreline reconstruction method by Bollerman et al (2014), which ensures better numerical stability at the wetting and drying fronts of a flood wave<ref ~~name="~~Bollerman~~"/>~~. An elaborate explanation is provided by Horváth et al. (2014)<ref ~~name="~~Horvath~~"/>~~.		This scheme is further extended with the shoreline reconstruction method by Bollerman et al (2014), which ensures better numerical stability at the wetting and drying fronts of a flood wave{{ref\|Bollerman}}. An elaborate explanation is provided by Horváth et al. (2014){{ref\|Horvath}}.

	General sequence of computational steps:		General sequence of computational steps:
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	\|references=		\|references=
	<references>		<references>
	<ref name=~~"Bollerman">~~Bollermann, Andreas & Chen, Guoxian & Kurganov, Alexander & Noelle, Sebastian. (2014)~~. A Well-balanced Reconstruction for Wetting, Drying Fronts. IGPM Report.~~ 313~~. ∙ found at:~~ https://www.researchgate.net/publication/269417532_A_Well-balanced_Reconstruction_for_Wetting_Drying_Fronts ~~(last visited:~~ 2019-07-24~~)</~~ref>		{{ref\|Bollerman
	~~<ref~~ name=~~"Horvath">~~Zsolt Horváth, Jürgen Waser, Rui A. P. Perdigão, Artem Konev and Günter Blöschl (2014) ~~∙ A two-dimensional numerical scheme of dry/wet fronts for the Saint-Venant system of shallow water equations ∙ found at:~~ http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.700.7977&rep=rep1&type=pdf ~~and https~~://~~www.vrvis~~.at/publications/~~pdfs/PB-VRVis-2014-034~~.pdf ~~(last visited 2024~~-03-~~15)</~~ref>		\|name=A Well-balanced Reconstruction for Wetting, Drying Fronts. IGPM Report
	~~<ref~~ name=~~"Kurganov2">Kurganov A, Petrova G (2007) ∙~~ A Second-Order Well-Balanced Positivity Preserving Central-Upwind Scheme for the Saint-Venant System ~~∙ found at:~~ http://www.math.tamu.edu/~gpetrova/KPSV.pdf ~~(last visited~~ 2019-04-11~~)</ref>~~		\|author=Bollermann, Andreas & Chen, Guoxian & Kurganov, Alexander & Noelle, Sebastian. (2014)
			\|page=313
			\|source=
			\|link=https://www.researchgate.net/publication/269417532_A_Well-balanced_Reconstruction_for_Wetting_Drying_Fronts
			\|lastvisit=2019-07-24
			}}
			{{ref\|Horvath
			\|name=A two-dimensional numerical scheme of dry/wet fronts for the Saint-Venant system of shallow water equations
			\|author=Zsolt Horváth, Jürgen Waser, Rui A. P. Perdigão, Artem Konev and Günter Blöschl (2014)
			\|page=
			\|source=
			\|link=http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.700.7977&rep=rep1&type=pdf, http://visdom.at/media/pdf/publications/Poster.pdf
			\|lastvisit=2018-06-29
			}}
			{{ref\|Kurganov2
			\|name=A Second-Order Well-Balanced Positivity Preserving Central-Upwind Scheme for the Saint-Venant System
			\|author=Kurganov A, Petrova G (2007)
			\|page=
			\|source=
			\|link=http://www.math.tamu.edu/~gpetrova/KPSV.pdf
			\|lastvisit=2019-04-11
			}}
	</references>		</references>
	}}		}}

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

Maxim@tygron.com at 10:18, 15 July 2025

2025-07-15T10:18:07Z

← Older revision		Revision as of 10:18, 15 July 2025
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	{{article end		{{article end
	\|notes=		\|notes=
	* Water can be added to and removed from the described surface system by the [[Rain model (Water Overlay)\|rain]], [[~~Evaporation~~ model (Water Overlay)\|~~evaporation~~]] and [[Infiltration model (Water Overlay)\|infiltration model]], as well as certain [[Hydraulic structures (Water Overlay)\|hydraulic structures]] and [[Breach (Water Overlay)\|breach]]es.		* Water can be added to and removed from the described surface system by the [[Rain model (Water Overlay)\|rain]], [[Evapotranspiration model (Water Overlay)\|evapotranspiration]] and [[Infiltration model (Water Overlay)\|infiltration model]], as well as certain [[Hydraulic structures (Water Overlay)\|hydraulic structures]] and [[Breach (Water Overlay)\|breach]]es.
	* In the case of [[Ground model (Water Overlay)\|subsurface flow]] a different flow system with different equations are used.		* In the case of [[Ground model (Water Overlay)\|subsurface flow]] a different flow system with different equations are used.
	* In addition to water flowing in between grid cells, water can also flow ''through'' [[Hydraulic structures (Water Overlay)\|hydraulic buildings]].		* In addition to water flowing in between grid cells, water can also flow ''through'' [[Hydraulic structures (Water Overlay)\|hydraulic buildings]].

← Older revision		Revision as of 12:06, 7 July 2026
Line 47:		Line 47:

	===Water level initialization===		===Water level initialization===
	In theory, each grid cell can have a unique bottom elevation and accompanying water depth, yielding a certain water surface elevation (or water level). ~~However, in~~ practice, water levels are often initialized for ~~large~~ groups of cells ~~rather than individual cells, assuming that each (water level) area in a project has been assigned a~~ [[water level (Water Overlay)\|water level]]. During the initialization phase a distinction is made between two types:		In theory, each grid cell can have a unique bottom elevation and accompanying water depth, yielding a certain water surface elevation (or water level). In practice, water levels are often initialized for groups of cells based on the [[water level (Water Overlay)\|water level]] assigned to each area. During the initialization phase a distinction is made between two types:
	* [[water level (Water Overlay)\|Water level]]s of [[Water area (Water Overlay)\|water areas]];		* [[water level (Water Overlay)\|Water level]]s of [[Water area (Water Overlay)\|water areas]];
	* [[inundation level (Water Overlay)\|Inundation level]]s of [[Inundation area (Water Overlay)\|inundation areas]].		* [[inundation level (Water Overlay)\|Inundation level]]s of [[Inundation area (Water Overlay)\|inundation areas]].

	For all [[Terrain water (Water Overlay)\|water ~~terrain~~]]s in a water area, the ~~volume of~~ water ~~per grid cell~~ is ~~such that the resulting water level at those locations conforms the value of~~ the [[Water level (Water Overlay)\|WATER_LEVEL]] attribute ~~as provided by~~ the corresponding [[Water area (Water Overlay)\|water area]].		For all [[Terrain water (Water Overlay)\|water terrains]] in a water area, the water level is set to the [[Water level (Water Overlay)\|WATER_LEVEL]] attribute of the corresponding [[Water area (Water Overlay)\|water area]].

	In contrast to water areas, which generate water on water terrains, inundation areas generate water over all grid cells, regardless of its terrain type. Similarly, the volume of water per grid cell is determined by the [[Inundation level (Water Overlay)\|INUNDATION_LEVEL]] attribute as provided by the corresponding inundation area.		In contrast to water areas, which generate water on water terrains, inundation areas generate water over all grid cells, regardless of its terrain type. Similarly, the volume of water per grid cell is determined by the [[Inundation level (Water Overlay)\|INUNDATION_LEVEL]] attribute as provided by the corresponding inundation area.