Replication of MACCA-GW: the ground water diffusion in an aquifer

Pierre Bommel, Bruno Bonté, Marie-Paule Bonnet, Grégoire Leclerc.

The aim of this model (zipfile, 191Ko) is to simulate water exchange between surface soil, river network and the underlying aquifer.
This model is a replication of the model by (Ravazzani et al. 2011) called MACCA-GW (for MACroscopic Cellular Automata for GroundWater).
It represents the water flow in unconfined aquifers. The full description of the model is availble on the Demo_Aquifer page.

Model description and results

The full description of the model is availble on the Demo_Aquifer page.
Here we configured the model in order to obtain the settings explained in Ravazzani et al. 2011.

Test 1: § 5.1 "Stability and convergence test"

The purpose is to test the stability and convergence of the aquifer. The aim of this analysis is to verify the method proposed by Ponce et al. (2001) to find the minimum value of time step that satisfies stability and convergence.
By default, it sets a 100x100 grid, with head = aHead m, except for the central zone where head = 25m.

Test 1a: "initRavazzaniTest1a": The initial head is set to 50 m (except for the central zone: 25m).
Test 1b: "initRavazzaniTest1b": The initial head is set to 100 m (except for the central zone: 25m).
Test 1c: "initRavazzaniTest1c": The initial head is set to 200 m (except for the central zone: 25m).
Test 1d: "initRavazzaniTest1d": The initial head is set to 400 m (except for the central zone: 25m).

Test 2 : § 5.2 "Steady flow between two streams in response to uniform recharge"

To run MACCA-GW, the model domain was set with two Dirichlet conditions on the west boundary (h₀ = 20 m) and the east boundary (h_L =17 m) to represent the stage in the river. In addition, a Neumann type B condition on north and south boundaries was considered. Recharge was set to 5.78704 10 9 m/s equivalent to 0.5 mm/day. The time step was set to 8000 s. Initial head was set to 17 m on every cell
T2 fig9 T2 cormas

Test 3 : § 5.3. "Drawdown due to a constant pumping rate from a well"

The domain was setup applying Dirichlet condition on the entire boundary with hydraulic head h = 50 m, as well as initial condition. A well with a constant pumping rate of 0.001 m3/s was placed in the central cell. The time step was set to 4000 s. Monitoring wells were placed along cardinal directions at a distance of 150, 200, 300 m from the pumping well. Two monitoring wells were placed on the 45 direction at a distance of 127 and 170 m to investigate the eventuality that von Neumann neighbourhood could generate privileged directions. A further monitoring well was positioned at the cell adjacent to the boundary to verify if boundary condition could have influence on the cone of depression. 12 days duration after the beginning of the pumping.
T3 grid

T3 results

Test 4 : § 5.4. "Aquifer response to stream-stage variation"

The domain was set up applying a constant head h = 50 m on the west and east boundaries, a Neumann type B condition on north and south boundaries, and an initial condition to perform the test. The time step was set to 4000 s. A river was placed with north- south direction at a distance of 250 m from the west boundary. River bottom was set at 46.5 m. Riverbed conductivity = 10^-5 m/s , thickness = 0.5 m, and width = 5 m. Monitoring wells were placed at a distance of 100, 350, 450, 550, and 650 m from the west boundary.

Computational performance

Duration of a simulation = 3 years (1095 days or time steps)

Test1ba (href=50m) : D = 1 => deltaT = 4000 - Daily repetition = 21
[sim_2018.05.01-18.08.38] was run in 606710 milliseconds, ie. 0 h: 10 m: 6.71 s.
Test1b (href=100m) : D = 1 => deltaT = 2000 - Daily repetition = 43
[sim_2018.05.01-18.28.58] was run in 1220382 milliseconds, ie. 0 h: 20 m: 20.382 s.
Test1c (href=200m) : D = 1 => deltaT = 1000 - Daily repetition = 86
[sim_2018.05.02-16.43.20] was run in 2174585 milliseconds, ie. 0 h: 36 m: 14.585 s.
Test1d (href=400m) : D = 1 => deltaT = 500 - Daily repetition = 172
[sim_2018.05.01-13.53.01] was run in 4.24114e6 milliseconds, ie. 1 h: 10 m: 50.171 s.

Even without display of the grid, the performances seem far below that of MACCA-GV (1.125 s) and MODFLOW (5.204 s), but the results on the performances are not clear (table 3).

For more information, see

Ravazzani, G., Rametta, D., & Mancini, M., 2011. Macroscopic cellular automata for groundwater modelling: A first approach. Environmental Modelling & Software, 26(5), 634-643. See paper on line

MODFLOW 6: Harbauch A W, 2005. Modflow-2005, The U.S. Geological Survey Modular Ground-Water Model, U.S. Geological Survey Techniques and Methods 6-A16 http://water.usgs.gov/nrp/gwsoftware/modflow2005/modflow2005.html

Download the model (zipfile, 191Ko)
For more information, contact the authors.