Difference between revisions of "Surface model (Water Overlay)"

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The [[Water Module]]'s primary function is the simulation of the 2-dimensional flow of water on the surface. In order to simulate flowing water, the project area is discretized into x by y cells, based on the configured [[grid cell size]].  
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==Computation==
 
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The [[Water Module]]'s primary function is simulating two-dimensional flow of water along 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, a set of rules is required that describes the behavior of the flow. This is done through 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):
Secondly a model is required which describes the rules that need to be followed. For this we use the two-dimensional Saint-Venant system, which reads:
 
 
[[File:2D-Saint-Venant_system.png|left]]
 
[[File:2D-Saint-Venant_system.png|left]]
where:
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where
: h<sub>t</sub> = height of water column on time t
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: h<sub>t</sub> = water depth at time t
: u<sub>t</sub> = flow speed in the x direction on time t
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: u<sub>t</sub> = velocity in the x direction at time t
: v<sub>t</sub> = flow speed in the y direction on time t
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: v<sub>t</sub> = velocity in the y direction at time t
 
: B<sub>x</sub> = slope in the x direction
 
: B<sub>x</sub> = slope in the x direction
 
: B<sub>y</sub> = slope in the y direction
 
: B<sub>y</sub> = slope in the y direction
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: g = gravitational constant
 
{{clear|left}}
 
{{clear|left}}
  
In the {{software}} this model is implemented using the ''Well Balanced Positivity Preserving Central-Upwind Scheme'' described in Kurganov and Petrova (2007)<ref name="Kurganov2"/>.
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[[File:Waterlevel_schematic.png|right|x200px|frame|For each grid cell:<br>B = bottom elevation<br>h = water depth<br>w = water surface elevation]]
For more information about the implementation, see [[Surface_flow_formula_(Water_Overlay)|Surface flow formula]].
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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''), rather than just the water depth (''h''). The image on the right aims to clarify on the various terms. More technical information on the {{software}}'s implementation of the ''Well-Balanced Positivity Preserving Central-Upwind Scheme'' can be found [[Surface_flow_formula_(Water_Overlay)|here]].
 
 
[[File:Waterlevel_schematic.png|right|x200px|frame|B = surface elevation of grid cell<br>h = water height of grid cell<br>w = water level of grid cell.]]
 
The implemented method rewrites the '''h''' from the original Saint-Venant system to <code>w = h + B</code>. See the image on the right for clarification on the terms water level (w), surface (or bottom) elevation (B) and water height (h).
 
  
 
====Flowing water====
 
====Flowing water====
Based on variations in the surface elevation and water levels, which may cause unbalance, water will start flowing, until it eventually is balanced in terms of water level and fluxes ''hu'' and ''hv''.
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Imbalances in the water surface elevation among grid cells drive the flow of water in the model until a state of equilibrium is reached in terms of ''w'' and flux.
 
 
{{clear|right}}
 
  
 
===Water level initialization===
 
===Water level initialization===
In theory, each grid cell can have a unique water level and accompanying water height. In practice though, water levels are often initialized for large groups of cells, since it is assumed that a particular area within the project area has a given [[water level (Water Overlay)|water level]]. Therefore, the surface water level is initialized based on hydrological features.
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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, 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:
We make the following distinction:  
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* [[water level (Water Overlay)|Water level]]s of [[Water level area (Water Overlay)|water level areas]];
* [[water level (Water Overlay)|Water level]]s of [[terrain water (Water Overlay)|water terrains]].
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* [[inundation level (Water Overlay)|Inundation level]]s of [[Inundation area (Water Overlay)|inundation areas]].
* [[inundation level (Water Overlay)|Potential water level]]s for inundated land.
 
 
 
For all [[Terrain water (Water Overlay)|water terrain]]s, the amount of water set on the grid cell is such that the resulting water level in that location is equal to the [[Water level (Water Overlay)|WATER_LEVEL]] attribute provided by the [[Water level area (Water Overlay)|Water level area]]. If no water level area is overlapping that grid cell, or the water level is below the [[terrain height (Water Overlay)|surface elevation]] of the grid cell, the water height is assumed to be 0 and the water level equal to the surface elevation.
 
 
 
For the second case, [[Inundation area (Water_Overlay)|inundation area]]s have been added to the model. Water is placed in all grid cells which are covered by an inundated area, (regardless of the terrain type in that location, in contrast to the water level areas), such that the resulting water level is again equal to the inundation area's [[Inundation level (Water Overlay)|INUNDATION_LEVEL]] attribute. If no inundation area is overlapping that grid cell, or the inundation level is below the surface elevation of the grid cell, the water height is assumed to be 0 and the water level equal to the surface elevation.
 
 
 
The terrain height is defined by the [[terrain height]] in the project. The surface height is further influenced by the height of constructions present in the project (bounded by [[Design flood elevation m model attribute (Water Overlay)|DESIGN_FLOOD_ELEVATION_M]]) and by the [[Breach height (Water Overlay)|BREACH_HEIGHT]] of [[Breach (Water Overlay)|breaches]].
 
  
==Notes==
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For all [[Terrain water (Water Overlay)|water terrain]]s in a water level 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 level area (Water Overlay)|water level area]].
* 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]], [[Sewer model (Water Overlay)|sewer]]s and [[Breach (Water Overlay)|breach]]es.
 
* Underground flow uses a different flow system and formula's, described in [[Underground model (Water Overlay)|underground model]].
 
* In addition to water flowing between adjacent grid cells, water can also flow through [[Hydraulic structures (Water Overlay)|hydraulic constructions]].
 
  
==Related formulas==
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In contrast to water level 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.
* [[Surface water level formula (Water Overlay)|Surface water level formula]]
 
* [[Surface flow formula (Water Overlay)|Surface flow formula]]
 
* [[Surface infiltration formula (Water Overlay)|Surface infiltration formula]]
 
  
* [[Culvert formula (Water Overlay)|Culvert formula]]
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If a grid cell is neither part of any water level 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 local [[terrain height]] of the project area, though it may be altered by the presence of a construction or the [[Breach height (Water Overlay)|BREACH_HEIGHT]] attribute of a [[Breach (Water Overlay)|breach]].
* [[Weir formula (Water Overlay)|Weir formula]]
 
* [[Breach growth formula (Water Overlay)|Breach growth formula]]
 
* [[Breach flow formula (Water Overlay)|Breach flow formula]]
 
* [[Pump formula (Water Overlay)|Pump formula]]
 
* [[Sewer Overflow formula (Water Overlay)|Sewer overflow formula]]
 
* [[Inlet formula (Water Overlay)|Inlet formula]]
 
  
==Related models==
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===Notes===
* [[Rain model (Water Overlay)|Rain model]]
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* 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.
* [[Evaporation model (Water Overlay)|Evaporation model]]
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* In the case of [[Underground model (Water Overlay)|subsurface flow]] a different flow system with different equations are used.
* [[Sewer model (Water Overlay)|Sewer model]]
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* In addition to water flowing in between grid cells, water can also flow ''through'' [[Hydraulic structures (Water Overlay)|hydraulic constructions]].
* [[Storage model (Water Overlay)|Storage model]]
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* The [[Design flood elevation m model attribute (Water Overlay)|DESIGN_FLOOD_ELEVATION_M]] attribute confines the maximum surface elevation induced by constructions.
* [[Substance flow model (Water Overlay)|Substance flow model]]
 
  
 
==References==
 
==References==

Latest revision as of 08:26, 11 July 2019

Computation

The Water Module's primary function is simulating two-dimensional flow of water along 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, a set of rules is required that describes the behavior of the flow. This is done through a second-order semi-discrete central-upwind scheme produced by Kurganov and Petrova (2007)[1], which is based on the 2-D Saint-Venant equations (a.k.a. shallow water equations):

2D-Saint-Venant system.png

where

ht = water depth at time t
ut = velocity in the x direction at time t
vt = velocity in the y direction at time t
Bx = slope in the x direction
By = slope in the y direction
g = gravitational constant
For each grid cell:
B = bottom elevation
h = water depth
w = water surface elevation

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), rather than just the water depth (h). The image on the right aims to clarify on the various terms. More technical information on the Tygron Platform's implementation of the Well-Balanced Positivity Preserving Central-Upwind Scheme can be found here.

Flowing water

Imbalances in the water surface elevation among grid cells drive the flow of water in the model until a state of equilibrium is reached in terms of w and flux.

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, assuming that each (water level) area in a project has been assigned a water level. During the initialization phase a distinction is made between two types:

For all water terrains in a water level 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 attribute as provided by the corresponding water level area.

In contrast to water level 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 attribute as provided by the corresponding inundation area.

If a grid cell is neither part of any water level area nor inundation area, or the assigned water level is lower than its 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 local terrain height of the project area, though it may be altered by the presence of a construction or the BREACH_HEIGHT attribute of a breach.

Notes

References

  1. 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)