Ground flow formula (Water Overlay): Difference between revisions
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<math>\Delta w_t = w_{1,t} - w_{2,t}</math> | <math>\Delta w_t = w_{1,t} - w_{2,t}</math> | ||
<math>B_{ | <math>B_{bb} = max ( B_{1}- d_{b,1} , B_{2}- d_{b,2} ) </math> | ||
<math>A_{c,t} = \Delta x \cdot ( \bar{w_{t}} - B_{ | <math>A_{c,t} = \Delta x \cdot ( \bar{w_{t}} - B_{bb} )</math> | ||
<math>K = min(K_{1} , K_{2} )</math> | <math>K = min(K_{1} , K_{2} )</math> | ||
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: <math>w_{n,t}</math> = The [[Groundwater level formula (Water Overlay)|ground water level]] of cell <math>n</math> at time <math>t</math>. | : <math>w_{n,t}</math> = The [[Groundwater level formula (Water Overlay)|ground water level]] of cell <math>n</math> at time <math>t</math>. | ||
: <math>B_c</math> = the datum height of the surface of cell c, set by the [[Elevation (Water Overlay)|elevation]] or a [[Terrain elevation prequel (Water Overlay)|Terrain elevation prequel]]. | : <math>B_c</math> = the datum height of the surface of cell c, set by the [[Elevation (Water Overlay)|elevation]] or a [[Terrain elevation prequel (Water Overlay)|Terrain elevation prequel]]. | ||
: <math>B_{ | : <math>B_{bb}</math> = the grid cell's edge datum height of the bottom boundary. | ||
: <math>K_n</math> = The hydraulic conductivity of the cell, defined in [[Terrain hydraulic conductivity md (Water Overlay)|HYDRAULIC_CONDUCTIVITY_MD]] of the ground terrain. | : <math>K_n</math> = The hydraulic conductivity of the cell, defined in [[Terrain hydraulic conductivity md (Water Overlay)|HYDRAULIC_CONDUCTIVITY_MD]] of the ground terrain. | ||
: <math>d_{b,c}</math> = The ground bottom distance of the cell c, defined by a [[Bottom distance prequel (Water Overlay)|Bottom distance prequel]] or a general [[Ground_bottom_distance_m_(Water_Overlay)|GROUND_BOTTOM_DISTANCE_M]] of the Water Overlay. | : <math>d_{b,c}</math> = The ground bottom distance of the cell c, defined by a [[Bottom distance prequel (Water Overlay)|Bottom distance prequel]] or a general [[Ground_bottom_distance_m_(Water_Overlay)|GROUND_BOTTOM_DISTANCE_M]] of the Water Overlay. | ||
Revision as of 12:53, 5 March 2024
Ground flow is different from surface flow, since it has to account for the slowdown and porousness of the medium. In general, horizontal ground flow is calculated using formulas described in Harbaugh 2005[1][2]. However, when an aquifer is present, the Aquifer formula is applied.
It depends on the configuration of the HYDRAULIC_CONDUCTIVITY_WITH_THICKNESS attribute value in the Water Overlay what Hydraulic Conductivity formula is used:
- A value means Hydraulic Conductivity without Thickness formula will be used.
- A value means Hydraulic Conductivity with Thickness formula will be used.
Hydraulic Conductivity without Thickness
The flow between the two cells is calculated as:
where:
- = The ground water level of cell at time .
- = the datum height of the surface of cell c, set by the elevation or a Terrain elevation prequel.
- = the grid cell's edge datum height of the bottom boundary.
- = The hydraulic conductivity of the cell, defined in HYDRAULIC_CONDUCTIVITY_MD of the ground terrain.
- = The ground bottom distance of the cell c, defined by a Bottom distance prequel or a general GROUND_BOTTOM_DISTANCE_M of the Water Overlay.
- = Area of conductance at time .
- = Ground water level difference at time .
- = Computational timestep.
- = Size of grid cell.
- = Averaged ground water level at time , based on water levels in ground, WATER_STORAGE_PERCENTAGE and potentially the surface water level, when the ground is filled to the top.
- = The amount of water to be transported at time between one cell and the other.
Hydraulic Conductivity with Thickness
The flow between the two cells is calculated as:
where:
- = The ground water level of cell at time .
- = The hydraulic conductivity of the cell, multiplied with the thickness of the layer, defined in HYDRAULIC_CONDUCTIVITY_WITH_THICKNESS_MD of the ground terrain.
- = Ground water level difference at time .
- = Computational timestep.
- = Size of grid cell.
- = The amount of water to be transported at time between one cell and the other.
Aquifer formula
When an aquifer is present, its hydraulic diffusivity is used to calculate the water flow.
Based on conditions being true, the calculated volume of water that is transported through the aquifer is calculated as:
Where:
- = Ground water level in cell at time ;
- = the datum height of the aquifer at the cell.
- = Volume in that flows between the two adjacent cells due to the aquifer at time .
- = Ground water level difference between the two adjacent cells at time ;
- = Computational timestep.
- = The AQUIFER_KD attribute of aquifer.
- = The calculated amount of water to be transported at time between one cell and the other.
Related
The following topics are related to this formula.
- Features
- Aquifer (Water Overlay)
- Formulas
- Groundwater level formula (Water Overlay)
- Ground infiltration formula (Water Overlay)
- Models
- Ground model (Water Overlay)
- Infiltration model (Water Overlay)
- Tracer flow model (Water Overlay)
See also
References
- ↑ 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.
- ↑ 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)
- Models
- Surface • Ground • Rain • Evaporation • Infiltration • Elevation • Breach • Sewer • Storage • Tracer flow • Border • Order
- Model formulas
- Timestep • Season • Surface water level • Groundwater level
- Flow formulas
- Surface flow • Surface infiltration • Ground flow • Ground infiltration • Surface evaporation • Ground evaporation • Ground bottom flow
- Hydraulic structure formulas
- Culvert • Weir • Breach growth • Breach flow • Pump • Sewer Overflow • Inlet • Drainage
- Related