Ground evaporation formula (Water Overlay): Difference between revisions

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Underground evaporation is calculated per cell.
Underground evaporation is calculated per cell.


For all underground evaporation, the height of the unsaturated zone is used.
For all underground evaporation calculation, the ground water depth at time t is used.
: ''H<sub>unsat</sub> = H<sub>surface</sub> - WL<sub>underground</sub>''
<math>d_{gw,t} = b_{s} - w_{g,t}</math>


First the capacity for saturated evaporation is calculated, based on how much of the saturated area is in contact with the roots.
Feddes oxygen stress factor:
: ''C<sub>sat</sub> = max( 0 , min( RD , GBDM ) - H<sub>unsat</sub> ) * WSP''
<math>f_o =
\begin{cases}
1.0 & \text{if } d_{gw,t} \text{ is } >= d_{r,3}} \\
\frac{d_{gw,t} -  d_{r,4}}{d_{r,3} - d_{r,4}} & \text{if } d_{gw,t} \text{ is } >= d_{r,4}} \\
0.0 & \text{otherwise} \\
\end{cases}
</math>


Next the height of the unsaturated zone, and based on that the capacity for unsaturated evaporation is calculated.
Feddes saturated zone root update factor:
: ''C<sub>unsat</sub> = max( 0 , min( RD , H<sub>unsat</sub> ) ) * ( W<sub>unsat</sub> / H<sub>unsat</sub> )''
<math>f_s =
\begin{cases}
0.0 & \text{if } d_{gw,t} \text{ is } >= 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 } >= d_{r,2}} \\
1.0 & \text{otherwise} \\
\end{cases}
</math>


Finally, the actual evaporation is calculated:
Max potential evaporation:
: ''Δw<sub>unsat</sub> = min( C<sub>unsat</sub> , Δt * E<sub>weather</sub> * E<sub>top</sub> )''
<math>E_{max} = f_t \cdot E_w \cdot f_o</math>
: ''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:
Evaporation unsaturated:
* Δw = The total amount of evaporation which takes place.
<math>E_{u} =  
* Δt = Computational timestep.
\begin{cases}
0.0 & \text{if } d_{us} \text{ is } <= 0.0} \\
min(E_{max}, h_u \cdot \frac{d_{r,1}}{d_{gw,t}})& \text{otherwise} \\
\end{cases}
</math>


* Δw<sub>unsat</sub> = The amount of evaporation which takes place from the unsaturated zone.
Evaporation saturated:
* Δw<sub>sat</sub> = The amount of evaporation which takes place from the saturated zone.
<math>h_{s} = w_{g,t} - ( b_{s} - d_{gb} )</math>
* C<sub>sat</sub> = The amount of evaporation that can take place from the saturated zone.
<math>h_{r} = max( 0.0 ,  w_{g,t} - ( b_{s} - d_{r,1} ))</math>
* C<sub>unsat</sub> = The amount of evaporation that can take place from the unsaturated zone.
<math>E_{sp} = (E_{max} - E_{u}) \cdot f_s</math>
* H<sub>unsat</sub> = The height (column) of the unsaturated zone.
<math>E_{s} = max (0.0 , min ( E_{sp}, h_{s}\cdot f_{gw}, h_r \cdot f_{gw}</math>
 
Evaporation total is the sum of evaporation in the saturated and unsaturated zone:
<math>E = E_u + E_s</math>
 
where
: <math>b_{s}</math> is the datum height of the surface.
: <math>w_{g}</math> is the underground water level.
: <math>d</math> is the column height of the unsaturated zone.
: <math>f_t</math> is the [[Water evaporation factor (Water Overlay)|transpiration factor]] of the buildings (plants) on the surface, or the surface terrain's
[Terrain_water_evaporation_factor_(Water_Overlay)|transpiration factor]] if none present.
: <math>E_{w,t}</math> is the [[Evaporation_m_(Water_Overlay)|evaporation rate]] of the [[weather]] at time t
: <math>f_0</math> is the feddes oxygen stress factor, calculated using the 3rd and 4th [[root depths (Water Overlay)|root depths]] and the feddes trapezium interpolation model and the ground water depth.


* 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.
* WL<sub>underground</sub> = The [[Groundwater level formula (Water Overlay)|groundwater level]], relative to {{datum}}.
* H<sub>surface</sub> = The [[Terrain height (Water Overlay)|terrain height]] in the cell, relative to {{datum}}.
* RD = The [[Root depth m (Water Overlay)|ROOT_DEPTH_M]] of the construction if present, the [[Terrain root depth m (Water Overlay)|ROOT_DEPTH_M]] of the surface terrain otherwise.
* GBDM = The [[Ground bottom distance m model attribute (Water Overlay)|GROUND_BOTTOM_DISTANCE_M]] of the Water Overlay. (effectively available height in the underground).
* E<sub>weather</sub> = The [[Evaporation_m_(Water_Overlay)|evaporation rate]] of the [[weather]].
* E<sub>top</sub> = The [[Water evaporation factor (Water Overlay)|WATER_EVAPORATION_FACTOR]] of the building (construction, plant) if present, the [[Terrain water evaporation factor (Water Overlay)|WATER_EVAPORATION_FACTOR]] of the surface terrain otherwise.


==Related==
==Related==

Revision as of 12:49, 25 February 2021

Underground evaporation is calculated per cell.

For all underground evaporation calculation, the ground water depth at time t is used. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d_{gw,t} = b_{s} - w_{g,t}}

Feddes oxygen stress factor: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f_o = \begin{cases} 1.0 & \text{if } d_{gw,t} \text{ is } >= d_{r,3}} \\ \frac{d_{gw,t} - d_{r,4}}{d_{r,3} - d_{r,4}} & \text{if } d_{gw,t} \text{ is } >= d_{r,4}} \\ 0.0 & \text{otherwise} \\ \end{cases} }

Feddes saturated zone root update factor: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f_s = \begin{cases} 0.0 & \text{if } d_{gw,t} \text{ is } >= 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 } >= d_{r,2}} \\ 1.0 & \text{otherwise} \\ \end{cases} }

Max potential evaporation: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_{max} = f_t \cdot E_w \cdot f_o}

Evaporation unsaturated: Failed to parse (unknown function "\begin{cases}"): {\displaystyle E_{u} = \begin{cases} 0.0 & \text{if } d_{us} \text{ is } <= 0.0} \\ min(E_{max}, h_u \cdot \frac{d_{r,1}}{d_{gw,t}})& \text{otherwise} \\ \end{cases} }

Evaporation saturated: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle h_{s} = w_{g,t} - ( b_{s} - d_{gb} )} Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle h_{r} = max( 0.0 , w_{g,t} - ( b_{s} - d_{r,1} ))} Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_{sp} = (E_{max} - E_{u}) \cdot f_s} Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_{s} = max (0.0 , min ( E_{sp}, h_{s}\cdot f_{gw}, h_r \cdot f_{gw}}

Evaporation total is the sum of evaporation in the saturated and unsaturated zone: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E = E_u + E_s}

where

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b_{s}} is the datum height of the surface.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle w_{g}} is the underground water level.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle d} is the column height of the unsaturated zone.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f_t} is the transpiration factor of the buildings (plants) on the surface, or the surface terrain's

[Terrain_water_evaporation_factor_(Water_Overlay)|transpiration factor]] if none present.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle E_{w,t}} is the evaporation rate of the weather at time t
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f_0} is the feddes oxygen stress factor, calculated using the 3rd and 4th root depths and the feddes trapezium interpolation model and the ground water depth.


Related

The following topics are related to this formula.

Formulas
Groundwater level formula
Models
Underground model
Evaporation model
Water Module
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Water Module
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Tutorials
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Overview
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Theory
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Benchmarks
Models
Surface • Ground • Rain • Evaporation • Infiltration • Elevation • Breach • Sewer • Storage • Tracer flow • Border • Order
Model formulas
Timestep • Season • Surface water level • Groundwater level
Flow formulas
Surface flow • Surface infiltration • Ground flow • Ground infiltration • Surface evaporation • Ground evaporation • Ground bottom flow
Hydraulic structure formulas
Culvert • Weir • Breach growth • Breach flow • Pump • Sewer Overflow • Inlet • Drainage
Related
Building attributes • Hydrological features • Hydraulic structures •  Terrain attributes • Model attributes • Results • Simulation data
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