Ground evaporation formula (Water Overlay): Difference between revisions

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Underground evaporation is calculated per cell.
Conceptually, water can evaporate from the ground via crop, tree and plant foliage. This is called evapotranspiration. The amount a plant can evaporate depends on the saturation and ground water level, as well as the root structure.
The [[Root depth m (Water Overlay)|factor by which roots]] can extract water from the ground is modeled using the Feddes trapezium.
[[File:Feddes_trapezium.jpg|thumb|right|400px|Feddes trapezium indicating for what water levels and by what factor roots of a plant can extract water from the ground.]]


Evaporation capacities:
The amount a plant, crop or tree evaporates also depends on its growth season. Therefore, the species specific [[Water evaporation (Function Value)|Water evaporation function value]] can be set as four [[Season formula (Water Overlay)|seasonal values]].


For all underground evaporation, the height of the unsaturated zone is used.
Last but not least, the calculated evapotranspiration factor is multiplied with the [[Evaporation m (Water Overlay)|evaporation amount]] at time <math>t</math>, which is configured for a [[Weather (Water Overlay)|Weather]].
: ''H<sub>unsat</sub> = H<sub>surface</sub> - WL<sub>underground</sub>''


First the capacity for saturated evaporation is calculated, based on how much of the saturated area is in contact with the roots.
The evaporated amount is first drawn from the unsaturated zone and then, when the expected amount is not yet reached, from the saturated zone.
: ''C<sub>sat</sub> = max( 0 , min( RD , GBDM ) - H<sub>unsat</sub> ) * WSP''


Next the height of the unsaturated zone, and based on that the capacity for unsaturated evaporation is calculated.
==Formulas==
: ''C<sub>unsat</sub> = max( 0 , min( RD , H<sub>unsat</sub> ) ) * ( W<sub>unsat</sub> / H<sub>unsat</sub> )''


Finally, the actual evaporation is calculated:
This evaporation is calculated per cell. For all ground evaporation calculation, the ground water depth at time t is used.
: ''Δw<sub>unsat</sub> = min( C<sub>unsat</sub> , Δt * E<sub>weather</sub> * E<sub>top</sub> )''
: ''Δw<sub>sat</sub> = min( C<sub>sat</sub> , (Δt * E<sub>weather</sub> * E<sub>top</sub>) - Δw<sub>unsat</sub> )''
: ''Δw = Δw<sub>unsat</sub> + Δw<sub>sat</sub>''


Where:
<math>d_{gw,t} = B_{c} - w_{g,t}</math>
* Δw = The total amount of evaporation which takes place.
* Δt = Computational timestep.


* Δw<sub>unsat</sub> = The amount of evaporation which takes place from the unsaturated zone.
Feddes oxygen stress factor:
* Δw<sub>sat</sub> = The amount of evaporation which takes place from the saturated zone.
* C<sub>sat</sub> = The amount of evaporation that can take place from the saturated zone.
* C<sub>unsat</sub> = The amount of evaporation that can take place from the unsaturated zone.
* H<sub>unsat</sub> = The height (column) of the unsaturated zone.


* W<sub>unsat</sub> = The amount of water in the saturated zone. The height of the water column if the equivalent amount of water was placed on the surface.
<math>f_o =
* WL<sub>underground</sub> = The groundwater level, relative to [[Datum|datum]].
\begin{cases}
* H<sub>surface</sub> = The terrain height in the cell, relative to datum.
1.0 & \text{if } d_{gw,t} \text{ is } \geq d_{r,3} \\
* RD = The [[Root depth m (Water Overlay)|ROOT_DEPTH_M]] of the construction if present, the ROOT_DEPTH_M of the surface terrain otherwise.
\frac{d_{gw,t} -  d_{r,4}}{d_{r,3} -  d_{r,4}} & \text{if } d_{gw,t} \text{ is } \geq d_{r,4} \\
* GBDM = The [[Ground bottom distance m model attribute (Water Overlay)|GROUND_BOTTOM_DISTANCE_M]] (effectively available height in the underground model).
0.0 & \text{otherwise}
* E<sub>weather</sub> = The [[Water evaporation factor (Water Overlay)|evaporation rate]] of the [[Weather|weather]].
\end{cases}
* E<sub>top</sub> = The [[Water evaporation factor (Terrain) (Water Overlay)|WATER_EVAPORATION_FACTOR]] of the construction if present, the WATER_EVAPORATION_FACTOR of the surface terrain otherwise.
</math>


{{Template:WaterOverlay_nav}}
Feddes saturated zone root update factor:
 
<math>f_s =
\begin{cases}
0.0 & \text{if } d_{gw,t} \text{ is } \geq d_{r,1} \\
1.0 - \frac{d_{gw,t} -  d_{r,2}}{d_{r,1} -  d_{r,2}} & \text{if } d_{gw,t} \text{ is } \geq d_{r,2} \\
1.0 & \text{otherwise}
\end{cases}
</math>
 
Seasonal transpiration factor:
 
<math> f_{ts,t} = (1.0 - f_{se,t}) \cdot f_{ts,c} + f_{se,t} \cdot f_{ts,n}</math>
 
Max potential evaporation:
 
<math>E_{max} = f_{ts,t} \cdot e_{w,t} \cdot f_o \cdot \Delta t</math>
 
Evaporation unsaturated:
 
<math>E_{u} =
\begin{cases}
0.0 & \text{if } d_{gw,t} \text{ is } \leq 0.0 \\
min(E_{max}, h_u \cdot \frac{d_{r,1}}{d_{gw,t}}) & \text{otherwise} \\
\end{cases}
</math>
 
Potential evaporation saturated:
 
<math>d_{s} = w_{g,t} - ( B_{c} - d_{b,c} )</math>
 
<math>d_{r} = max( 0.0 ,  w_{g,t} - ( B_{c} - d_{r,1} ))</math>
 
<math>E_{p,s} = (E_{max} - E_{u}) \cdot f_s</math>
 
Evaporation saturated zone:
 
<math>E_{s} = max (0.0 , min ( E_{p,s}, d_{s}\cdot f_{ws}, d_r \cdot f_{ws}) ) </math>
 
Evaporation total is the sum of evaporation in the saturated and unsaturated zone:
 
<math>E_g = E_u + E_s</math>
 
where
: <math>B_{c}</math> = the datum height of the surface of cell c, set by the [[Elevation (Water Overlay)|elevation]] or a [[Terrain elevation prequel (Water Overlay)|Terrain elevation prequel]].
: <math>w_{g,t}</math> = the ground water level (datum height) at time t.
: <math>d_{gw,t}</math> = the depth of the ground water level, which is equal to the column height of the unsaturated zone at time t.
: <math>f_{ts,c}</math> = the [[Water evaporation factor (Water Overlay)|transpiration factor]] at current season c, of the buildings (plants) on the surface, or the surface terrain's [[Terrain_water_evaporation_factor_(Water_Overlay)|transpiration factor]] if none present.
: <math>f_{ts,n}</math> = the [[Water evaporation factor (Water Overlay)|transpiration factor]] at coming season n, of the buildings (plants) on the surface, or the surface terrain's [[Terrain_water_evaporation_factor_(Water_Overlay)|transpiration factor]] if none present.
: <math>f_{se,t}</math> = [[Season formula (Water Overlay)|Season fraction]]. Used for interpolating the transpiration factor.
: <math>f_{ts,t}</math> =  Can be supplied as four values; it is an interpolated value based on the current and next season.
: <math>e_{w,t}</math> = the [[Evaporation_m_(Water_Overlay)|evaporation rate]] of the [[weather]] at time t.
: <math>f_o</math> = the calculated feddes oxygen stress factor, calculated using the 3rd and 4th [[Root_depth_m_(Water_Overlay)|root depths]] and the feddes trapezium interpolation model and the ground water depth.
: <math>f_s</math> = the calculated feddes saturated zone root update factor, calculated using the 1st and 2nd [[Root_depth_m_(Water_Overlay)|root depths]] and the feddes trapezium interpolation model and the ground water depth.
: <math>\Delta t</math> = the computational [[Timestep formula (Water Overlay)|timestep]] in seconds.
: <math>d_{b,c}</math> = The ground bottom distance of the cell c, defined by a [[Bottom distance prequel (Water Overlay)|Bottom distance prequel]] or a general [[Ground_bottom_distance_m_(Water_Overlay)|GROUND_BOTTOM_DISTANCE_M]] of the Water Overlay.
: <math>d_{s}</math> = the column height of the saturated zone covered by the roots.
: <math>d_{r,n}</math> = the nth [[Root_depth_m_(Water_Overlay)|root depth value]].
: <math>h_u</math> = the amount of water in the unsaturated zone.
: <math>E_{max}</math> = the potential max evaporation.
: <math>E_{u}</math> = the evaporation in the unsaturated zone.
: <math>E_{p,s}</math> = the potential evaporation in the saturated zone.
: <math>f_{ws}</math> = The [[Terrain water storage percentage (Water Overlay)|WATER_STORAGE_PERCENTAGE]] of the ground terrain type, used here as a fraction.
: <math>E_{s}</math> = the evaporation in the saturated zone.
: <math>E_{g}</math> = the total evaporation from the ground.
 
==Related==
The following topics are related to this formula.
; Formulas
: [[Groundwater level formula (Water Overlay)]]
; Models
: [[Ground model (Water Overlay)]]
: [[Evaporation model (Water Overlay)]]
 
{{article end
|notes=
* The ground water level cannot be lowered further than the defined root depth by evapotranspiration.
}}
{{WaterOverlay formula nav}}

Latest revision as of 14:07, 5 March 2024

Conceptually, water can evaporate from the ground via crop, tree and plant foliage. This is called evapotranspiration. The amount a plant can evaporate depends on the saturation and ground water level, as well as the root structure. The factor by which roots can extract water from the ground is modeled using the Feddes trapezium.

Feddes trapezium indicating for what water levels and by what factor roots of a plant can extract water from the ground.

The amount a plant, crop or tree evaporates also depends on its growth season. Therefore, the species specific Water evaporation function value can be set as four seasonal values.

Last but not least, the calculated evapotranspiration factor is multiplied with the evaporation amount at time , which is configured for a Weather.

The evaporated amount is first drawn from the unsaturated zone and then, when the expected amount is not yet reached, from the saturated zone.

Formulas

This evaporation is calculated per cell. For all ground evaporation calculation, the ground water depth at time t is used.

Feddes oxygen stress factor:

Feddes saturated zone root update factor:

Seasonal transpiration factor:

Max potential evaporation:

Evaporation unsaturated:

Potential evaporation saturated:

Evaporation saturated zone:

Evaporation total is the sum of evaporation in the saturated and unsaturated zone:

where

= the datum height of the surface of cell c, set by the elevation or a Terrain elevation prequel.
= the ground water level (datum height) at time t.
= the depth of the ground water level, which is equal to the column height of the unsaturated zone at time t.
= the transpiration factor at current season c, of the buildings (plants) on the surface, or the surface terrain's transpiration factor if none present.
= the transpiration factor at coming season n, of the buildings (plants) on the surface, or the surface terrain's transpiration factor if none present.
= Season fraction. Used for interpolating the transpiration factor.
= Can be supplied as four values; it is an interpolated value based on the current and next season.
= the evaporation rate of the weather at time t.
= the calculated feddes oxygen stress factor, calculated using the 3rd and 4th root depths and the feddes trapezium interpolation model and the ground water depth.
= the calculated feddes saturated zone root update factor, calculated using the 1st and 2nd root depths and the feddes trapezium interpolation model and the ground water depth.
= the computational timestep in seconds.
= The ground bottom distance of the cell c, defined by a Bottom distance prequel or a general GROUND_BOTTOM_DISTANCE_M of the Water Overlay.
= the column height of the saturated zone covered by the roots.
= the nth root depth value.
= the amount of water in the unsaturated zone.
= the potential max evaporation.
= the evaporation in the unsaturated zone.
= the potential evaporation in the saturated zone.
= The WATER_STORAGE_PERCENTAGE of the ground terrain type, used here as a fraction.
= the evaporation in the saturated zone.
= the total evaporation from the ground.

Related

The following topics are related to this formula.

Formulas
Groundwater level formula (Water Overlay)
Models
Ground model (Water Overlay)
Evaporation model (Water Overlay)

Notes

  • The ground water level cannot be lowered further than the defined root depth by evapotranspiration.