Ground infiltration formula (Water Overlay): Difference between revisions

Latest revision as of 13:49, 5 March 2024

Water can infiltrate from the unsaturated zone to the saturated zone.

The infiltration from the unsaturated zone to the saturated zone is calculated per cell.

First the height of the unsaturated zone is calculated.

d_{u}=B_{c}-w_{g}

Then the ratio of water amount to unsaturated height is calculated.

r=\Delta w_{u}/d_{u}

Then we calculate the distance of the unsaturated zone which can infiltrate.

d_{i}=min(d_{u},\Delta t\cdot f_{i,t}\cdot I_{g})

Finally, we calculate the actual amount of water that infiltrates from the unsaturated zone to the saturated zone.

\Delta w_{i}=d_{i}\cdot r

Where:

w_{g}

B_{c}

= the datum height of the surface of cell c, set by the elevation or a Terrain elevation prequel.

d_{u}

= The height of the unsaturated zone.

\Delta w_{u}

= The amount of water in the unsaturated zone. The height of the water column if the equivalent amount of water was placed on the surface.

r

= Ratio of water to height in the unsaturated zone.

\Delta t

= Computational timestep in seconds.

f_{i,t}

= The interpolated infiltration factor at time

t

I_{g}

= The GROUND_INFILTRATION_MD of the underground terrain type.

d_{i}

= The height distance in the unsaturated zone which can be subject to infiltration to the saturated zone.

\Delta w_{i}

= The infiltration which takes place from the unsaturated zone to the saturated zone.

@@ Line 9: / Line 9: @@
 Then we calculate the distance of the unsaturated zone which can infiltrate.
-: <math>d_{i} = min( d_{u} , \Delta t \cdot I_{g} )</math>
+: <math>d_{i} = min( d_{u} , \Delta t \cdot f_{i,t} \cdot I_{g} )</math>
 Finally, we calculate the actual amount of water that infiltrates from the unsaturated zone to the saturated zone.
@@ Line 20: / Line 20: @@
 : <math>\Delta w_u</math> = The amount of water in the unsaturated zone. The height of the water column if the equivalent amount of water was placed on the surface.
 : <math>r</math> = Ratio of water to height in the unsaturated zone.
-: <math>\Delta t</math> = Computational timestep.
+: <math>\Delta t</math> = Computational [[Timestep formula (Water Overlay)|timestep]] in seconds.
+: <math>f_{i,t}</math> = The interpolated infiltration factor at time <math>t</math>. Configured using [[Infiltration_factor_s_(Water_Overlay)|INFILTRATION_FACTOR_S]].
 : <math>I_{g}</math> = The [[Terrain ground infiltration md (Water Overlay)|GROUND_INFILTRATION_MD]] of the underground terrain type.
 : <math>d_{i}</math> = The height distance in the unsaturated zone which can be subject to infiltration to the saturated zone.