Breach growth formula (Water Overlay) and Breach (Water Overlay): Difference between pages

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Water can flow through [[breach (Water Overlay)|breach]]es into levee protected areas. These breaches often start small and grow over time<ref name="breachgrow"/>.  
A breach is a modification to the [[terrain height (Water Overlay)|terrain height]], with an optional in- or outflow of water for the hydrological model. This can be used to represent calamitous situations, such as a breach in a levee. Breaches can also be used to easily simulate a terrain height increase, like a levee.


The water flowing through breaches can originate from an external area outside the project area or an input area within the project area.
A breach can either be defined solely as a terrain height modification using its [[Breach_height_(Water_Overlay)|BREACH_HEIGHT]] attribute, or as a connection to a water body outside of the hydrological model by adding attributes related to the external water body. If the breach is only defined as a terrain height change, only water that is already created or defined in some other way in the hydrological model can flow through and from it.


First, the difference in height of the water on either side of the breach is calculated.
If the breach is given the attributes required for the external water body, water will automatically be created or removed uniformly on the breach, depending on the simulated water body "behind" the breach.  


: ''Δh = abs( max(0, w<sub>e</sub> - H<sub>b,t</sub>) - max(0, w<sub>b,t</sub> - H<sub>b,t</sub>) )''
The breach can grow over time, based on its initial width and the critical speed at which water may flow. If a [[Breach_width_(Water_Overlay)|BREACH_WIDTH]] is defined, the breach's polygon is intersected with a circle emanating from the centerpoint of the polygon. It is only in that intersection, dubbed the "active breach", that water will flow in from the simulated external water body. The radius of the circle defining the intersection will expand as water flows, based on the critical speed of the water as defined in the [[Breach_speed_(Water_Overlay)|BREACH_SPEED]] attribute. All cells in the active breach are considered directly adjacent to the external water body.


Using the height difference, the breach width increase is calculated.
The [[terrain height (Water Overlay)|terrain]] covered by the entire breach area is considered lowered to the height defined by its [[Breach_height_(Water_Overlay)|BREACH_HEIGHT]] attribute, even if the active breach does not extend across the entirety of the breach area.


: ''ΔW<sub>b,t</sub> = f<sub>m</sub> * (g<sup>1/2</sup> * Δh<sup>3/2</sup> / cs<sub>b</sub> ) * log<sub>10</sub> (1 + (0.04 * g / cs<sub>b</sub> ) * Δt / 3600)''
Water flowing through or across a breach will flow in the direction defined by the [[Breach_angle_(Water_Overlay)|BREACH_ANGLE]] attribute, regardless of whether the water flowed onto the breach from elsewhere in the water model, or from the simulated external water body. If no [[Breach_angle_(Water_Overlay)|BREACH_ANGLE]] is defined, water can flow in any direction.


The current breach width is then equal to the last calculated breach width, plus the calculated breach width increment.
If no critical speed is defined, the active breach will never grow. If no width is defined, the width is assumed to be very large, creating an intersection exactly the size of the polygon.


: ''W<sub>b,t</sub> = W<sub>b,t-1</sub> + ΔW<sub>b,t</sub>''
{{Overlay attribute
 
|attribute=[[Breach_height_(Water_Overlay)|BREACH_HEIGHT]]
Where:
|unit={{mdatum}}
* W<sub>b</sub> = The [[Breach width (Water Overlay)|BREACH_WIDTH]] of the breach.
|description=The new [[terrain height]] at the location of the breach.  
* H<sub>b,t</sub> = The [[Breach height (Water Overlay)|BREACH_HEIGHT]] of the breach at time t.
|defaultvalue=n/a
* W<sub>b,t</sub> = The calculated breach width, initially equal to W<sub>b</sub>.
|icon=[[File:waterwizard_icon_breach_height.png]]
* w<sub>b,t</sub> = water level at breach at time t.
|attribute2=[[Breach_width_(Water_Overlay)|BREACH_WIDTH]]
* w<sub>e,t</sub> = water level at entry area (external or internal) at time t.
|unit2=m
* Δh<sub>t</sub> = The difference between the height of the water columns on either side of the breach at time t.
|description2=The initial width of the breach.
* f<sub>m</sub> = Material factor, set to 1.3 (average for sand and clay levees).
|defaultvalue2=10000
* g = Acceleration factor of [[Gravity (Water Overlay)|GRAVITY]], defined for the Water Overlay.
|icon2=[[File:waterwizard_icon_breach_width.png]]
* cs<sub>b</sub> = The critical [[Breach speed (Water Overlay)|BREACH_SPEED]] of the breach.
|attribute3=[[Breach_angle_(Water_Overlay)|BREACH_ANGLE]]
* ΔW<sub>b,t</sub> = The calculated width increase of the breach at time t.
|unit3={{geoangle}}
* Δt = Computational timestep.
|description3=The angle at which water can flow from the breach.  
 
|defaultvalue3=n/a
==Notes==
|icon3=[[File:waterwizard_icon_breach_angle.png]]
* The breach height H<sub>b,t</sub> can be defined over time, by configuring the [[Breach height (Water Overlay)|BREACH_HEIGHT]] as an [[attribute array]].
|attribute4=[[Breach_speed_(Water_Overlay)|BREACH_SPEED]]
 
|unit4=m/s
==Related==
|description4=The critical speed factor in the [[Breach_growth_formula_(Water_Overlay)|Breach width grow-formula]].
The following topics are related to this formula.
|defaultvalue4=n/a
; Features
|icon4=[[File:waterwizard_icon_breach_speed.png]]
: [[Breach (Water Overlay)|Breach]]
|attribute5=[[External_surface_level_(Water_Overlay)|EXTERNAL_SURFACE_LEVEL]]
; Formulas
|unit5={{mdatum}}
: [[Breach flow formula (Water Overlay)|Breach flow formula]]
|description5=The height of the bottom of the external water body behind the breach. The lowest level the external water level can lower to.
; Models
|defaultvalue5=0
: [[Surface model (Water Overlay)|Surface model]]
|icon5=[[File:waterwizard_icon_external_surface_level.png]]
 
|attribute6=[[External_water_level_(Water_Overlay)|EXTERNAL_WATER_LEVEL]]
==References==
|unit6={{mdatum}}
<references>
|description6=The water level of the external water body behind the breach. The initial level the water level is set to.
<ref name="breachgrow">Verheij, H.J. ∙ Aanpassen van het bresgroeimodel in HIS-OM: Bureaustudie ∙ found at: http://resolver.tudelft.nl/uuid:aedc8109-da43-4a03-90c3-44f706037774 ∙ (last visited 2019-03-08)</ref>
|defaultvalue6=0
</references>
|icon6=[[File:waterwizard_icon_external_water_level.png]]
 
|attribute7=[[External_area_(Water_Overlay)|EXTERNAL_AREA]]
{{Template:WaterOverlay_nav}}
|unit7=m²
|description7=The surface area of the external water body behind the breach. The larger the external water body, the more water can flow from it, and the smaller the effect of the inflow or outflow of water on the external water level.
|defaultvalue7=n/a
|icon7=[[File:waterwizard_icon_external_surface_level.png]]
|attribute8=[[Breach_input_area_(Water_Overlay)|BREACH_INPUT_AREA]]
|unit8=Item ID
|description8=The [[Area]] representing the influx area for the breach.
|defaultvalue8=none
|icon8=[[File:waterwizard_icon_breach_input_area.png]]
}}
{{WaterOverlay hydrological features nav}}
{{Water Module buttons}}
{{Water Module buttons}}

Revision as of 13:52, 19 June 2019

A breach is a modification to the terrain height, with an optional in- or outflow of water for the hydrological model. This can be used to represent calamitous situations, such as a breach in a levee. Breaches can also be used to easily simulate a terrain height increase, like a levee.

A breach can either be defined solely as a terrain height modification using its BREACH_HEIGHT attribute, or as a connection to a water body outside of the hydrological model by adding attributes related to the external water body. If the breach is only defined as a terrain height change, only water that is already created or defined in some other way in the hydrological model can flow through and from it.

If the breach is given the attributes required for the external water body, water will automatically be created or removed uniformly on the breach, depending on the simulated water body "behind" the breach.

The breach can grow over time, based on its initial width and the critical speed at which water may flow. If a BREACH_WIDTH is defined, the breach's polygon is intersected with a circle emanating from the centerpoint of the polygon. It is only in that intersection, dubbed the "active breach", that water will flow in from the simulated external water body. The radius of the circle defining the intersection will expand as water flows, based on the critical speed of the water as defined in the BREACH_SPEED attribute. All cells in the active breach are considered directly adjacent to the external water body.

The terrain covered by the entire breach area is considered lowered to the height defined by its BREACH_HEIGHT attribute, even if the active breach does not extend across the entirety of the breach area.

Water flowing through or across a breach will flow in the direction defined by the BREACH_ANGLE attribute, regardless of whether the water flowed onto the breach from elsewhere in the water model, or from the simulated external water body. If no BREACH_ANGLE is defined, water can flow in any direction.

If no critical speed is defined, the active breach will never grow. If no width is defined, the width is assumed to be very large, creating an intersection exactly the size of the polygon.

Template:Overlay attribute

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Group
Water area
Water level • Water relative
Sewer area
Sewer storage • Sewer pump speed
Inundation area
Inundation level
Aquifer
Aquifer kd • Aquifer datum
Breach
Breach height • Breach width • Breach angle • Breach coefficient • Breach speed • Breach input area • Breach level area • External surface level • External water level • External area
Rain area
Rain m
Limitation area
Limit area
Output
Object flow output • Object height output • Object datum output a • Object datum output b • Object width output
Related
Building attributes • Hydraulic structures •  Terrain attributes • Model attributes • Results • Simulation data


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