Ground flow formula (Water Overlay): Difference between revisions

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<math>A_{c} = \Delta x \cdot ( w_{avg} - B_{ex} )</math>
<math>A_{c} = \Delta x \cdot ( w_{avg} - B_{ex} )</math>


<math>C = min(C_{1} , C_{2} )</math>
<math>K = min(K_{1} , K_{2} )</math>


<math>q = \Delta w \cdot C \cdot A_{c} / \Delta x \cdot \Delta t</math>
<math>q = \Delta w \cdot K \cdot A_{c} / \Delta x \cdot \Delta t</math>


where:
where:
: <math>w_n</math> = The [[Groundwater level formula (Water Overlay)|underground water level]] of cell n.
: <math>w_n</math> = The [[Groundwater level formula (Water Overlay)|underground water level]] of cell n.
: <math>B_n</math> = The [[terrain height (Water Overlay)|surface height]] of cell n.
: <math>B_n</math> = The [[terrain height (Water Overlay)|surface height]] of cell n.
: <math>C_n</math> = The hydraulic conductivity of the cell, defined in [[Terrain hydraulic conductivity md (Water Overlay)|HYDRAULIC_CONDUCTIVITY_ND]] of the underground terrain.
: <math>K_n</math> = The hydraulic conductivity of the cell, defined in [[Terrain hydraulic conductivity md (Water Overlay)|HYDRAULIC_CONDUCTIVITY_ND]] of the underground terrain.
: <math>D_{ground}</math> = The configured ground bottom distance, defined in [[Ground_bottom_distance_m_(Water_Overlay)|GROUND_BOTTOM_DISTANCE_M]] of the Water Overlay.  
: <math>D_{ground}</math> = The configured ground bottom distance, defined in [[Ground_bottom_distance_m_(Water_Overlay)|GROUND_BOTTOM_DISTANCE_M]] of the Water Overlay.  
: <math>A_c</math> = Area of conductance.
: <math>A_c</math> = Area of conductance.

Revision as of 16:11, 18 December 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 hydraulic conductivity of the cell, defined in HYDRAULIC_CONDUCTIVITY_ND 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 following condition is checked in order to allow water movement through the aquifer:

Based on this condition being true, the transported volume V is calculated:


Where:

= Ground water level in the cell;
= the height of the aquifer at the cell.
= Volume in that flows between the two adjacent cells due to the aquifer.
= Ground water level difference between the two adjacent cells;
= Computational timestep.
= The AQUIFER_KD attribute of aquifer.

Related

The following topics are related to this formula.

Features
Aquifer
Formulas
Groundwater level formula
Underground infiltration formula
Models
Underground model
Infiltration model
Tracer flow model

See also

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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