Terrain height and Weir formula (Water Overlay): Difference between pages

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{{learned|about Terrain Height|how terrain height is implemented in the {{software}}|how to add or remove terrain height with the terrain height brush panel|how to change terrain height}}
Flow across [[Weir (Water Overlay)|weir]]s is calculated differently for free flow and submerged flow.


==Terrain height==
The height of the water at each end of the weir, relative to the weir, is calculated:
: Terrain height is the whole of differences of terrain elevation in a given area, the quantitative measurement of vertical elevation change in a landscape. Terrain is used here as a general term in physical geography, referring to the lay of the land. This is usually expressed in terms of the elevation, slope, and orientation of terrain features. Terrain height - as element of a terrain - affects surface water flow and distribution. Over a large area, it can affect weather and climate patterns.
: ''h<sub>s</sub> = max(0, max( w<sub>l</sub>, w<sub>r</sub> ) - z<sub>w</sub>)''
: ''h<sub>d</sub> = max(0, min( w<sub>l</sub>, w<sub>r</sub> ) - z<sub>w</sub>)''


: In overlays, the user can select two types of elevation, the digital terrain model (DTM) and digital surface model (DSM). A DTM represents the bare ground surface without any objects like plants and buildings. In contrast; a DSM represents the earth's surface including all objects (e.g. houses, trees, etc.) on it.
Based on the relative water heights, the weir is judged to have either a submerged flow or a free flow, based on the following ratio:
: ''h<sub>ratio</sub> = h<sub>d</sub> / h<sub>s</sub>''
:: C = min( C<sub>submerged</sub> , C<sub>free</sub>) if h<sub>ratio</sub> &gt; 0,5
:: C = C<sub>free</sub> otherwise


: [[File:DTM_DSM.png|400px]]
For free flow, capacity is calculated directly:
: <math>C_{free} = f_{w,d} * c_w * w_w \cdot ( h_s - h_d )^{3/2}</math>


: View original file here:[https://commons.wikimedia.org/wiki/File:DTM_DSM.svg]
For submerged flow, the following calculation is used:
: <math>C_{submerged} = U_{loss} \cdot A \cdot \sqrt{ 2 \cdot g \cdot ( h_s - h_d ) }</math>


==Terrain height in the {{software}}==
Finally the actual amount of water flow is calculated:
: ''Δw = ''Δt * C / Δx''


===DTM for projects in The Netherlands===
Where:
* h<sub>s</sub> = The height of the water column relative to the top of the weir, on the side with the highest [[Surface water level formula (Water Overlay)|water level]].
* h<sub>d</sub> = The height of the water column relative to the top of the weir, on the side with the lowest [[Surface water level formula (Water Overlay)|water level]].
* w<sub>l</sub> = The water level on the left side of the weir, relative to {{datum}}.
* w<sub>r</sub> = The water level on the right side of the weir, relative to {{datum}}.
* z<sub>w</sub> = The [[Weir height (Water Overlay)|WEIR_HEIGHT]] of the weir.
* f<sub>w,d</sub> = Dutch weir factor, set to 1.7.
* c<sub>w</sub> = The [[Weir coefficient (Water Overlay)|WEIR_COEFFICIENT]] of the weir.
* w<sub>w</sub> = The [[Weir width (Water Overlay)|WEIR_WIDTH]] of the weir.
* C = The potential rate of water flow across the weir.
* h<sub>ratio</sub> = The ratio of water heights on either side of the culvert.
* C<sub>free</sub> = The potential rate of water flow across the weir, based on a free flow calculation.
* C<sub>submerged</sub> = The potential rate of water flow across the weir, based on a submerged calculation.
* U<sub>loss</sub> = Loss coefficient for submerged weirs, set to 0.9.
* A = Flow area, based on the highest water column height relative to the top of the weir, and [[Weir width (Water Overlay)|WEIR_WIDTH]] of the weir.
* g = Acceleration factor of [[Gravity (Water Overlay)|GRAVITY]], defined for the Water Overlay.
* Δw = The water flow which takes place.
* Δt = Computational timestep.
* Δx = Cell size.


====Data sources====
==Related==
In the Netherlands a DTM is constructed using the following data sources:
The following topics are related to this formula.
* A base DTM, with a cell size of 3mx3m, supplied by Rijkswaterstaat to [http://www.arcgis.com/home/item.html?id=58a541efc59545e6b7137f961d7de883 ESRI], based on the AHN2.
; Structures
* A DSM from [http://www.arcgis.com/home/item.html?id=55df27e20c0d42e3a8bd48bc74c5c8cc AHN2] or [http://www.arcgis.com/home/item.html?id=b87c68ea246c4b17807cdad486279a47 AHN3] raw data ([http://www.ahn.nl Actuele Hoogte Bestand]) with a cell-size of 0.5x0.5m, 1x1m or 2.5x2.5m.
: [[Weir_(Water_Overlay)|Weir]]
* A DTM from [http://www.arcgis.com/home/item.html?id=9d62ff8889ba41b2b712a68c7493bd16 AHN2] or [http://www.arcgis.com/home/item.html?id=9d62ff8889ba41b2b712a68c7493bd16 AHN3] containing interpolated ("maailveld") data from ESRI, with a cell-size of 0.5x0.5m, 1x1m or 2.5x2.5m.
; Models
* [][https://www.pdok.nl/nl/producten/pdok-downloads/basisregistratie-topografie/topnl/topnl-actueel/top10nl Top10NL] data.
: [[Surface model (Water Overlay)|Surface model]]


When defining a new project, you can choose whether the project should use AHN2 or AHN3 the DSM resolution under the [[Advanced options|'''Advanced Options''']] at the [[wizard]]. These options influence the generation of the DTM:
{{Template:WaterOverlay_nav}}
* ''Use AHN3 DSM'': if selected the AHN3 will be used, if not selected the AHN2.
* The AHN data will be available on 0.5m, 1m or 2.5m resolution in the project database for generating the elevation grid (see the image below).
 
[[File:Ahn.jpg|600px]]
 
====DTM generation====
By the following steps a project DTM is composed:
* The ESRI DTM and DSM are resampeled to the same resolution
* The difference between the resampeled DTM and DSM is computed
* Depending on the topography-value and a threshold either the value of the DTM or DSM is used to compose a DTM on high resolution:
** for bare lands the default threshold is 100cm, all cells with a difference <100cm between the DTM and DSM, the value will be taken from the DSM
** for roads the default threshold is 25cm, all cells with a difference <25cm between the DTM and DSM, the value will be taken from the DSM
** for crop-lands, scrup-land, etc the default threshold is 50cm, all cells with a difference <50cm between the DTM and DSM, the value will be taken from the DSM
It is possible to change the default thresholds. Therefore, change the corresponding value in the [[Advanced options|'''Advanced Options''']] menu (see the image below). The first value is for bare lands, the second for the roads and the third for the crop-lands etc. <br>
[[File:Advanced_settings.JPG|600px]]
* Rooftops of buildings are getting an average height of the DSM of the polygon defining the buildings footprint. The footprint is split into sections using image recognition techniques; herewith the variability in rooftops can be taken into account in the elevation model
 
====Waterdepth====
Water bodies, found in [[terrain]] surface types, are lowered a few meters relative to the elevation of the surrounding surface.
By default:
*Boezemwater: 3m lowered relative to the elevation of the surrounding surface
*Water: 2m lowered relative to the elevation of the surrounding surface
These values can be changed by changing the WATER_DEPTH_M attribute of the Terrain type.
From the DEM a heightpoint in or as close to the wateredge is taken. On that point the Underground terrain type is determined. The slope (talud) of the sides of the water body is defined by the ANGLE_OF_REPOSE of this [[Terrain#Subsurface|Underground Terrain Types]] and the maximum depth to which a water body is carved out is WATER_DEPTH_M as defined for the surface terrain type on this point. If the angle of repose is shallow enough and the water body thin enough, the angled sides may meet up before the maximum water depth is reached. In this case the water body will be appropriately shallower.
The ANGLE_OF_REPOSE attribute can also be changed.
 
==Changing terrain height==
There are two options to change terrain height. One is to import a raster file with the new terrain height and the other option is to draw in the {{software}} where the terrain should be changed and to which height.
 
===Importing a terrain height dataset===
See [[How_to_import_terrain_height_data| how to import terrain height data]].
 
<br clear=all>
 
<!--
==Adding or removing terrain height==
{{Editor location|Terrain elevation}}[[File:TerrainHeightBrushPanel1.jpg|thumb|right|200px|Drawing Terrain Height in 3D world]]
: When a project is created in the {{software}}, all terrain is flat. To add relief in the form of terrain height, a specific tool is available - the height tool brush.
 
===The Terrain Height Brush panel===
{{Editor location|Terrain elevation}}
: Below is an image of the Terrain Height Brush Panel. This tool looks like the more common [[brush|brush panel]], but is adjusted to be able to draw in terrain height in the [[3D World|3D world]].
[[File:TerrainHeightBrushPanel2.jpg|left|frame|200px|Terrain Height Brush Panel]]<br clear=all>
====Start/ stop drawing====
: ''The top button on the panel is called "Start Drawing" by default when loading the panel. This first button (de)activates the Terrain Height brush panel, by selecting the button named "Start Drawing" the rest of the options become available on the panel. With the brush panel activated, the user can start "painting". Selecting this button again - now named "Stop Drawing" - deactivates the panel, greying out the options.''
<gallery mode="nolines">
File:TerrainHeightBrushPanel3.jpg|Terrain height brush panel inactive
File:TerrainHeightBrushPanel2.jpg|Terrain height brush panel active
</gallery>
 
====Radius====
: ''The first slider from the top is called "Radius". The radius slider refers to how big the area is that the cursor will affect when changing the terrain's height. The more to the right the slider is positioned, the larger the area of effect is.''
<gallery mode="nolines">
File:TerrainHeightBrushPanelRadius.jpg|Terrain height brush panel radius slider
</gallery>
 
====Press====
: ''The second slider from the top is called "Press" - for "Pressure". The press slider refers to how fast the area will be affected when changing the terrain's height. The more to the right the slider is positioned, the faster the area will adjust, making it possible to quickly alter terrain. If the slider is positioned more to the left side, the height effect can be finely adjusted.''
<gallery mode="nolines">
File:TerrainHeightBrushPanelPress.jpg|Terrain height brush panel press slider
</gallery>
====Brush Types====
----
 
=====Flatten=====
: ''The brush type button on the right of the "Clear" button is called "Flatten". With the "Flatten" button, any area that the brush 'paints' will be flattened while maintaining most of its height. This is useful when placing constructions on elevated or lowered terrain, as constructions can only be placed on flat surfaces.''
<gallery mode="nolines">
File:TerrainHeightBrushPanelFlatten.jpg|Terrain height brush panel flatten button
</gallery>
 
=====Raise=====
: ''The brush type button below the "Clear" button is called "Raise". With the "Raise" button any area that the brush 'paints' will be raised in elevation, in order to create terrain height, such as hills or other relief.
<gallery mode="nolines">
File:TerrainHeightBrushPanelRaise.jpg|Terrain height brush panel raise button
</gallery>
 
=====Lower=====
: ''The brush type button below the "Flatten" button is called "Lower". With the "Lower" button any area that the brush 'paints' will be lowered in elevation, in order to create terrain effects such as valleys or even open (polder) water.''
<gallery mode="nolines">
File:TerrainHeightBrushPanelLower.jpg|Terrain height brush panel lower button
</gallery>
----
 
====Reset Changes====
: ''The next button is called "Reset Changes". This button makes it possible to quickly undo any changes. With this button any changes that are not applied yet will be reverted.''
<gallery mode="nolines">
File:TerrainHeightBrushPanelResetChanges.jpg|Terrain height brush panel reset changes button
</gallery>
 
====Apply Changes====
: ''The last button, on the bottom of the panel, is called "Apply Changes". This button confirms changes made with the terrain height brush. After applying these changes it is not possible to revert them anymore. ''
<gallery mode="nolines">
File:TerrainHeightBrushPanelApplyChanges.jpg|Terrain height brush panel apply changes button
</gallery>
-->
 
===Drawing terrain height===
{{Editor location|Terrain elevation}}
{{Editor steps|title=change terrain height|Open the Terrain Height Brush Panel|Select "Start Drawing"|Adjust the Radius and Press sliders as desired|Select the brush type Raise, Flatten or Lower|Adjust terrain height by pressing and holding the left mouse button while drawing in the 3D world| Confirm the changes by selecting "Apply changes"}}
 
<!--===Removing terrain height===
{{Editor location|Terrain elevation}}
{{Editor steps|title=remove terrain height|Open the Terrain Height Brush Panel|Select "Start Drawing"|Adjust the Radius and Press sliders as desired|Select the brush type Clear|Adjust terrain height by pressing and holding the left mouse button while drawing in the 3D world| Confirm the changes by selecting "Apply changes"}}-->

Revision as of 10:49, 20 March 2020

Flow across weirs is calculated differently for free flow and submerged flow.

The height of the water at each end of the weir, relative to the weir, is calculated:

hs = max(0, max( wl, wr ) - zw)
hd = max(0, min( wl, wr ) - zw)

Based on the relative water heights, the weir is judged to have either a submerged flow or a free flow, based on the following ratio:

hratio = hd / hs
C = min( Csubmerged , Cfree) if hratio > 0,5
C = Cfree otherwise

For free flow, capacity is calculated directly:

For submerged flow, the following calculation is used:

Finally the actual amount of water flow is calculated:

Δw = Δt * C / Δx

Where:

  • hs = The height of the water column relative to the top of the weir, on the side with the highest water level.
  • hd = The height of the water column relative to the top of the weir, on the side with the lowest water level.
  • wl = The water level on the left side of the weir, relative to datum.
  • wr = The water level on the right side of the weir, relative to datum.
  • zw = The WEIR_HEIGHT of the weir.
  • fw,d = Dutch weir factor, set to 1.7.
  • cw = The WEIR_COEFFICIENT of the weir.
  • ww = The WEIR_WIDTH of the weir.
  • C = The potential rate of water flow across the weir.
  • hratio = The ratio of water heights on either side of the culvert.
  • Cfree = The potential rate of water flow across the weir, based on a free flow calculation.
  • Csubmerged = The potential rate of water flow across the weir, based on a submerged calculation.
  • Uloss = Loss coefficient for submerged weirs, set to 0.9.
  • A = Flow area, based on the highest water column height relative to the top of the weir, and WEIR_WIDTH of the weir.
  • g = Acceleration factor of GRAVITY, defined for the Water Overlay.
  • Δw = The water flow which takes place.
  • Δt = Computational timestep.
  • Δx = Cell size.

Related

The following topics are related to this formula.

Structures
Weir
Models
Surface model

Template:WaterOverlay nav