Ground evaporation formula (Water Overlay): Difference between revisions

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. $d_{gw,t}=b_{s}-w_{g,t}$

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 (unknown function "\begin{cases}"): {\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: $E_{max}=f_{t}\cdot E_{w}\cdot f_{o}$

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: $h_{s}=w_{g,t}-(b_{s}-d_{gb})$ $h_{r}=max(0.0,w_{g,t}-(b_{s}-d_{r,1}))$ $E_{sp}=(E_{max}-E_{u})\cdot f_{s}$ $E_{s}=max(0.0,min(E_{sp},h_{s}\cdot f_{gw},h_{r}\cdot f_{gw}$

Evaporation total is the sum of evaporation in the saturated and unsaturated zone: $E=E_{u}+E_{s}$

where

b_{s}

is the datum height of the surface.

w_{g}

is the underground water level.

d

is the column height of the unsaturated zone.

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.

E_{w,t}

is the evaporation rate of the weather at time t

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.

Ground evaporation formula (Water Overlay): Difference between revisions

Revision as of 12:49, 25 February 2021

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@@ Line 1: / Line 1: @@
 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}
+.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 & \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 & \text{if } d_{gw,t} \text{ is } >= d_{r,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}} \\
+.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 & \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.
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Ground evaporation formula (Water Overlay): Difference between revisions

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