Bottom flow pankow benchmark (Water Module): Difference between revisions

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: <math>h_2</math>: measured ground water level (m) at <math>x_2</math>
: <math>h_2</math>: measured ground water level (m) at <math>x_2</math>
: <math>h_d</math>: seepage head
: <math>h_d</math>: seepage head
: <math>K</math>: horizontal infiltration speed of the freatic layer (m/day)
: <math>KD</math>: measured horizontal transmissivity of the ground layer (m2/day)
: <math>D</math>: horizontal infiltration speed (m / day)
: <math>N</math>: additional ground water due to rainfall (m/day).
: <math>N</math>: additional ground water due to rainfall (m/day).
: <math>\epsilon</math>: accepted error margin
: <math>\epsilon</math>: accepted error margin


===Setup===
===Setup===
The following setup has been taken from the use case ''Peilverschil over een strook grond (freatisch)'' at [http://grondwaterformules.nl/index.php/formules/peilverschil/rechte-strook-freatisch grondwaterformules.nl].
We setup the following situation. The grid size used is 53 by 5, with a configurable cell size of <math>dx<\math> in meters. There are two waterways, left and right, both with a stable water level of 3 meters.


In the situation described there, the chosen Length L is set to 500 m. This is achieved with a grid size of 28 by 5, with a cell size of 20 m. There are two stable ground water levels, one on left of 11 meters (datum) and one on the right at 10 meters (datum). The rainfall is 0.8 mm per day, the horizontal infiltration speed is 3 m per day.
One inlet is placed on the cells x = 1 and y = 1 to 3 and an other is placed on the cells x = 52 and y - 1 to 3, with the following setup to ensure a stable water level:
:[[Inlet_upper_threshold_(Water_Overlay)|UPPER_THRESHOLD]] set to 3 m.
:[[Inlet_lower_threshold_(Water_Overlay)|LOWER_THRESHOLD]] set to 3 m.
:[[Inlet q (Water Overlay)|Inlet Q]] set to 0, such that is unlimited.


The terrain height is set to:
<math>\begin {cases}
0, & \text{if }x < 4 \text{ or } x > 48\\
1.5, & \text{if }x == 4 \text{ or } x == 48\\
3.5, & \text{if }x == 5 \text{ or } x == 47\\
5, & \text{otherwise}
\end{cases}</math>


The terrain height is set to 12 for all cells and the [[Ground bottom distance m (Water Overlay)|ground bottom distance]] is also set to 12.
An aquifer can be added to configure the [[Aquifer KD (Water Overlay)|horizontal infiltration speed]]. An important thing to note here, is that the KD value used in the report <ref name="Pankow68"/> is derived from changes in water head over time, and does not mention the storage capacity of the soil. Therefor, in order to configure the Aquifer KD value in the {{software}}, the KD value has to be multiplied with the storage percentage.
 
The terrain type's [[Ground infiltration md (Water Overlay)|infiltration speed]] can be configured to 3 m / day.


For x = 1 the initial ground water level is set to 11 and for x = 26 the ground water level is set to 10. The initial ground water levels between this points is linearly interpolated.
For x = 1 the initial ground water level is set to 11 and for x = 26 the ground water level is set to 10. The initial ground water levels between this points is linearly interpolated.

Revision as of 13:56, 15 December 2020

This testcase demonstrates a situation where a parcel of land is situated between two waterways with a stable water level. In combination with seepage, a characteristic curve will form over time, as shown in the image below. It is described in a water balance research in 1968 of Pankow and Rijtema [1], and also contain the accompanying formulas that describe the curve. In this case, we use the case which does not take into account the additional water flow resistance of the waterway. Secondly, rain could also be taken into account, but we set that to 0 to exclusively benchmark the seepage mechanics. The continuous rainfall case is already tested in freatic groundwater levels benchmark.

A parcel of land situated between two waterways with seepage and optional continuous rainfall

Formulas

Due to seepage and two stable water levels left and right, a specific ground water table curve will form. Part of the water seeped in will flow left and part of the it will flow right. Note that the time at which this balance occurs is dependent on the starting situation.

The following formula, taken from [1], describes the curve of ground water levels when the ground water flow to the left and right have become stable:

Simplified without rain N:

To test the correctness of the seepage, the formula can test the following condition with the accepted error margin :

where:

: distance (m) of the point of measurement compared to the middle of the parcel.
: distance (m) of the second point of measurement, which is always situated 3 meters from the edge of the waterway.
: measured ground water level (m) at
: measured ground water level (m) at
: seepage head
: measured horizontal transmissivity of the ground layer (m2/day)
: additional ground water due to rainfall (m/day).
: accepted error margin

Setup

We setup the following situation. The grid size used is 53 by 5, with a configurable cell size of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle dx<\math> in meters. There are two waterways, left and right, both with a stable water level of 3 meters. One inlet is placed on the cells x = 1 and y = 1 to 3 and an other is placed on the cells x = 52 and y - 1 to 3, with the following setup to ensure a stable water level: :[[Inlet_upper_threshold_(Water_Overlay)|UPPER_THRESHOLD]] set to 3 m. :[[Inlet_lower_threshold_(Water_Overlay)|LOWER_THRESHOLD]] set to 3 m. :[[Inlet q (Water Overlay)|Inlet Q]] set to 0, such that is unlimited. The terrain height is set to: <math>\begin {cases} 0, & \text{if }x < 4 \text{ or } x > 48\\ 1.5, & \text{if }x == 4 \text{ or } x == 48\\ 3.5, & \text{if }x == 5 \text{ or } x == 47\\ 5, & \text{otherwise} \end{cases}}

An aquifer can be added to configure the horizontal infiltration speed. An important thing to note here, is that the KD value used in the report [1] is derived from changes in water head over time, and does not mention the storage capacity of the soil. Therefor, in order to configure the Aquifer KD value in the Tygron Platform, the KD value has to be multiplied with the storage percentage.

For x = 1 the initial ground water level is set to 11 and for x = 26 the ground water level is set to 10. The initial ground water levels between this points is linearly interpolated.

Additionally, two underground inlets are placed, one on x=1 and one on x=26, as an area over y = 1 to 3.

The simulation time is set to n days, with a rainfall of 0.8 mm per day. To configure this, the rain set is set to .

Results

365 days

The first result is generated for n = 365:
Benchmark freatic 365.png

730 days

The second result is generated using n = 730:
Benchmark freatic 730.png

Notes

  • The amount of days it takes to reach the stable solution is highly dependent on the starting situation.

References

  1. 1.0 1.1 1.2 Cite error: Invalid <ref> tag; no text was provided for refs named Pankow68

Cite error: <ref> tag with name "Bear79" defined in <references> is not used in prior text.