Ground flow formula (Water Overlay)

Underground flow is different from surface flow, since it has to account for the slowdown and porousness of the medium. In general, horizontal underground flow is calculated using formulas described in Harbaugh 2005. However, when an aquifer is present, the aquifer variant is applied.

Default horizontal flow

Two adjacent cells, where underground water level of cell 1 is larger than cell 2.

The flow between the two cells is calculated as:

$\Delta w=w_{1}-w_{2}$

$B_{ex}=max(B_{1},B_{2})-D_{ground}$

$A_{c}=\Delta x\cdot (w_{avg}-B_{ex})$

$C=min(C_{1},C_{2})$

$q=\Delta w\cdot C\cdot A_{c}/\Delta x\cdot \Delta t$

where:

$w_{n}$ = The underground water level of cell n.

$B_{n}$ = The surface height of cell n.

$C_{n}$ = The ground conductance of cell, defined in GROUND_INFILTRATION_MD of the underground terrain.

$D_{ground}$ = The configured ground bottom distance, defined in GROUND_BOTTOM_DISTANCE_M of the Water Overlay.

$A_{c}$ = Area of conductance.

$\Delta w$ = Underground water level difference.

$\Delta t$ = Computational timestep.

$\Delta x$ = Size of grid cell.

$w_{avg}$ = Averaged underground water level, based on water levels in underground, WATER_STORAGE_PERCENTAGE and potentially the surface water level, when the underground is filled to the top.

Aquifer formula

When an aquifer is present, its hydraulic diffusivity is used to calculate the water flow.

First, the hydraulic diffusivity dictates the fraction of the water height difference which will flow.

F = 2 * sqrt( KD / WSP_source ) * sqrt( Δt ) * ( 1 / cell )

Based on this fraction, the actual amount of water flow is calculated.

Failed to parse (syntax error): {\displaystyle \Delta w = ( \frac{WL_{source}}{WSP_{source}) - (WL_{target}/WSP_{source}) ) * F}

} Where:

• $\Delta w$ = The underground flow which takes place.
• $\Delta t$ = Computational timestep.
• $cell$ = Cell size.

• F = Fraction of water which flows between cells

• KD = The AQUIFER_KD attribute of aquifer.
• WSP_source = The WATER_STORAGE_PERCENTAGE attribute of the underground terrain type of the origin cell.
• WSP_target = The WATER_STORAGE_PERCENTAGE attribute of the underground terrain type of the target cell.
• WL_source = The amount of water in the saturated zone of the source cell. The height of the water column if the equivalent amount of water was placed on the surface.
• WL_target = The amount of water in the saturated zone of the target cell. The height of the water column if the equivalent amount of water was placed on the surface.

See also

• Underground horizontal flow

Related

The following topics are related to this formula.

Features

Aquifer

Formulas

Groundwater level formula

Underground infiltration formula

Models

Underground model

Infiltration model

Substance flow model