Ground flow formula (Water Overlay): Difference between revisions

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First, the hydraulic diffusivity dictates the fraction of the water height difference which will flow.
First, the hydraulic diffusivity dictates the fraction of the water height difference which will flow.
: <math>F = 2 \cdot \sqrt{\frac{ KD}{ s_s}} \cdot \sqrt{ \Delta t } \cdot \frac{1}{dx}</math>
: <math>V = \Delta gw \cdot KD \cdot \Delta t</math>


Based on this fraction, the actual amount of water flow is calculated.
Based on this fraction, the actual amount of water flow is calculated.
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Where:
Where:
 
: <math>V</math> = Volume in <math>m{3}</math> that flows between the two cells due to the aquifer.
: <math>gw_s</math> = The water level 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.
: <math>gw_t</math> = The water level 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.
: <math>\Delta gw</math> = The underground flow which takes place.
: <math>\Delta t</math> = Computational timestep.
: <math>\Delta t</math> = Computational timestep.
: <math>dx</math> = Cell size.
: <math>F</math> = Fraction of water which flows between cells
: <math>KD</math> = The [[Aquifer kd (Water Overlay)|AQUIFER_KD]] attribute of aquifer.
: <math>KD</math> = The [[Aquifer kd (Water Overlay)|AQUIFER_KD]] attribute of aquifer.
: <math>s_s</math> = The [[Terrain water storage percentage (Water Overlay)|WATER_STORAGE_PERCENTAGE]] attribute of the underground terrain type of the origin cell.
: <math>s_t</math> = The [[Terrain water storage percentage (Water Overlay)|WATER_STORAGE_PERCENTAGE]] attribute of the underground terrain type of the target cell.


==See also==
==See also==

Revision as of 16:17, 24 January 2020

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[1][2]. 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:

where:

= The underground water level of cell n.
= The surface height of cell n.
= The ground conductance of cell, defined in GROUND_INFILTRATION_MD of the underground terrain.
= The configured ground bottom distance, defined in GROUND_BOTTOM_DISTANCE_M of the Water Overlay.
= Area of conductance.
= Underground water level difference.
= Computational timestep.
= Size of grid cell.
= 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.

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

Where:

= Volume in that flows between the two cells due to the aquifer.
= Computational timestep.
= The AQUIFER_KD attribute of aquifer.

See also

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

References

  1. ↑ Harbaugh, A.W., 2005, MODFLOW-2005, the U.S. Geological Survey modular ground-water model-the Ground-Water Flow Process: U.S. Geological Survey Techniques and Methods 6-A16, variously paginated.
  2. ↑ Langevin, C.D., Hughes, J.D., Banta, E.R., Niswonger, R.G., Panday, Sorab, and Provost, A.M. (2017) ∙ Documentation for the MODFLOW 6 Groundwater Flow Model: U.S. Geological Survey Techniques and Methods, book 6, chap. A55 ∙ p 31 ∙ found at: https://doi.org/10.3133/tm6A55 (last visited 2019-02-04)

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