Ground evaporation formula (Water Overlay): Difference between revisions

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Max potential evaporation:
Max potential evaporation:


<math>E_{max} = f_t \cdot E_w \cdot f_o</math>
<math>E_{max} = f_t \cdot E_{w,t} \cdot f_o</math>


Evaporation unsaturated:
Evaporation unsaturated:
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<math>E_{u} =
<math>E_{u} =
\begin{cases}
\begin{cases}
0.0 & \text{if } d_{us} \text{ is } \geq 0.0 \\
0.0 & \text{if } d_{gw,t} \text{ is } \geq 0.0 \\
min(E_{max}, h_u \cdot \frac{d_{r,1}}{d_{gw,t}}) & \text{otherwise} \\
min(E_{max}, h_u \cdot \frac{d_{r,1}}{d_{gw,t}}) & \text{otherwise} \\
\end{cases}
\end{cases}
</math>
</math>


Evaporation saturated:
Potential evaporation saturated:


<math>h_{s} = w_{g,t} - ( b_{s} - d_{gb} )</math>
<math>d_{s} = w_{g,t} - ( b_{s} - d_{gb} )</math>


<math>h_{r} = max( 0.0 ,  w_{g,t} - ( b_{s} - d_{r,1} ))</math>
<math>d_{r} = max( 0.0 ,  w_{g,t} - ( b_{s} - d_{r,1} ))</math>


<math>E_{sp} = (E_{max} - E_{u}) \cdot f_s</math>
<math>E_{p,s} = (E_{max} - E_{u}) \cdot f_s</math>


<math>E_{s} = max (0.0 , min ( E_{sp}, h_{s}\cdot f_{gw}, h_r \cdot f_{gw}</math>
Evaporation saturated zone
<math>E_{s} = max (0.0 , min ( E_{p,s}, d_{s}\cdot f_{gw}, d_r \cdot f_{gw}</math>


Evaporation total is the sum of evaporation in the saturated and unsaturated zone:
Evaporation total is the sum of evaporation in the saturated and unsaturated zone:
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where  
where  
: <math>b_{s}</math> is the datum height of the surface.
: <math>b_{s}</math> is the datum height of the surface.
: <math>w_{g}</math> is the underground water level.
: <math>w_{g,t}</math> is the ground water level (datum height) at time t.
: <math>d</math> is the column height of the unsaturated zone.
: <math>d_{gw,t}</math> is the depth of the ground water level, which is equal to the column height of the unsaturated zone at time t.
: <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
: <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.
[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>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.
: <math>f_o</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.
 
: <math>f_s</math> is the feddes saturated zone root update factor, calculated using the 1st and 2nd [[root depths (Water Overlay)|root depths]] and the feddes trapezium interpolation model and the ground water depth.
: <math>d_{r,n}</math> is the nth [[root depths (Water Overlay)|root depth value]].
: <math>E_{max}</math> is the potential max evaporation
: <math>E_{u}</math> is the evaporation in the unsaturated zone
: <math>E_{p,s}</math> is the potential evaporation in the saturated zone
: <math>E_{s}</math> is the evaporation in the saturated zone
: <math>d_{gb}</math> is the [[ground bottom distance]]
: <math>d_{s}</math> is the column height of the saturated zone covered by the roots


==Related==
==Related==

Revision as of 13:33, 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 } \geq d_{r,3} \\ \frac{d_{gw,t} - d_{r,4}}{d_{r,3} - d_{r,4}} & \text{if } d_{gw,t} \text{ is } \geq 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 } \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} }

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,t} \cdot f_o}

Evaporation unsaturated:

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_{u} = \begin{cases} 0.0 & \text{if } d_{gw,t} \text{ is } \geq 0.0 \\ min(E_{max}, h_u \cdot \frac{d_{r,1}}{d_{gw,t}}) & \text{otherwise} \\ \end{cases} }

Potential 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 d_{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 d_{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_{p,s} = (E_{max} - E_{u}) \cdot f_s}

Evaporation saturated 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_{s} = max (0.0 , min ( E_{p,s}, d_{s}\cdot f_{gw}, d_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,t}} is the ground water level (datum height) 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 d_{gw,t}} is the depth of the ground water level, which is equal to the column height of the unsaturated zone 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_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_o} 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.
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} is the 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.
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_{r,n}} is the nth root depth value.
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}} is the potential max 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_{u}} is the evaporation in 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 E_{p,s}} is the potential evaporation in the saturated 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_{s}} is the evaporation in the saturated 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 d_{gb}} is the ground bottom distance
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_{s}} is the column height of the saturated zone covered by the roots

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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