Linearized Unconfined 1D Periodic Recharge#
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This case validates the transient linearized Boussinesq-Dupuit response of an unconfined 1D aquifer submitted to a sinusoidal recharge forcing.
Case Setup#
geometry: quasi-1D Cartesian grid (50 x 5, single layer),
flow regime: transient unconfined flow,
west/east boundaries: fixed at 10.0 m,
recharge forcing: 5.0 + 5.0 * sin(2Ï€ t / 10 d) mm/day sampled every 1 day,
initial condition: uniform 10.0 m,
simulated observable: watertable_elevation.
Available solver variants: MODFLOW-NWT, MODFLOW 6, MODFLOW 6 irregular triangles, Boussinesq.
What It Shows#
Periodic recharge forcing and phase/amplitude propagation in transient flow
Primary metrics: space-time RMSE, space-time max abs error, final-profile RMSE, cross-row spread.
Solver-specific figures and metrics are shown side by side so the same benchmark can be read across backends.
Analytical Reference#
Linearized transient response to sinusoidal recharge
Solver Coverage#
Default solver: MODFLOW-NWT
Available variants: MODFLOW-NWT, MODFLOW 6, MODFLOW 6 irregular triangles, Boussinesq
Metrics - Space-time RMSE: 0.0078 m - Space-time max abs error: 0.0194 m - Final-profile RMSE: 0.0010 m - Cross-row head spread: 9.99e-06 m
Config file:
validation_cases/analytical/transient/linearized_unconfined_recharge_periodic_1d/config_modflownwt.tomlTolerances:
validation_cases/analytical/transient/linearized_unconfined_recharge_periodic_1d/tolerances.tomlExpected output: 40 periods, spatial shape 5 x 50
python -m validation_cases.analytical.transient.linearized_unconfined_recharge_periodic_1d.run_case --no-show --solver modflow_nwt
Metrics - Space-time RMSE: 0.0065 m - Space-time max abs error: 0.0167 m - Final-profile RMSE: 0.0009 m - Cross-row head spread: 8.19e-07 m
Config file:
validation_cases/analytical/transient/linearized_unconfined_recharge_periodic_1d/config_modflow6.tomlTolerances:
validation_cases/analytical/transient/linearized_unconfined_recharge_periodic_1d/tolerances_modflow6.tomlExpected output: 40 periods, spatial shape 5 x 50
python -m validation_cases.analytical.transient.linearized_unconfined_recharge_periodic_1d.run_case --no-show --solver modflow6
Metrics - Space-time RMSE: 0.0066 m - Space-time max abs error: 0.0167 m - Final-profile RMSE: 0.0010 m - Cross-row head spread: 0.00e+00 m
Config file:
validation_cases/analytical/transient/linearized_unconfined_recharge_periodic_1d/config_modflow6_irregular_tri.tomlTolerances:
validation_cases/analytical/transient/linearized_unconfined_recharge_periodic_1d/tolerances_modflow6_irregular_tri.tomlExpected output: 40 periods, spatial shape 5 x 50
python -m validation_cases.analytical.transient.linearized_unconfined_recharge_periodic_1d.run_case --no-show --solver modflow6_irregular_tri
Metrics - Space-time RMSE: 0.0024 m - Space-time max abs error: 0.0063 m - Final-profile RMSE: 0.0002 m - Cross-row head spread: 1.38e-15 m
Config file:
validation_cases/analytical/transient/linearized_unconfined_recharge_periodic_1d/config_boussinesq.tomlTolerances:
validation_cases/analytical/transient/linearized_unconfined_recharge_periodic_1d/tolerances.tomlExpected output: 40 periods, spatial shape 5 x 50
python -m validation_cases.analytical.transient.linearized_unconfined_recharge_periodic_1d.run_case --no-show --solver boussinesq
Reproduce#
Run the underlying example or validation case with:
python -m validation_cases.analytical.transient.linearized_unconfined_recharge_periodic_1d.run_case --no-show
Refresh the committed gallery artifacts with:
python -m tools.doc_gallery
Case Parameters#
Reference Parameters#
Field |
Meaning |
Value |
Source |
|---|---|---|---|
|
Minimum x coordinate of the analytical reference domain. |
0 |
|
|
Maximum x coordinate of the analytical reference domain. |
100 |
|
|
Baseline hydraulic head around which the linearized reference is expressed. |
10 m |
|
|
Mean recharge applied in the periodic reference forcing. |
5 mm/day |
|
|
Amplitude of the periodic recharge forcing used by the reference solution. |
5 mm/day |
|
|
Period of the periodic forcing used by the reference solution. |
10 days |
|
|
Phase shift applied to the periodic reference forcing. |
0 rad |
|
|
Hydraulic conductivity used by the analytical or benchmark reference. |
0.0001 m/s |
|
|
Reference saturated thickness used by the linearized formulation. |
10 m |
|
|
Specific yield used by the transient reference formulation. |
0.1 - |
|
|
Axis along which the validation profile is extracted. |
0 |
|
|
Number of terms retained in the analytical series expansion. |
400 |
|
|
Reference time step used by the analytical evaluator. |
86400 s |
|
Common Numerical Setup#
Field |
Meaning |
Value |
Source |
|---|---|---|---|
|
Case-specific configuration field workflow used by the validation benchmark. |
simulation |
|
|
Simulation start time used by the benchmark. |
2003-01-01 00:00:00 |
|
|
Simulation end time used by the benchmark. |
2003-02-09 00:00:00 |
|
|
Nominal time step used by the benchmark. |
1 day |
|
|
Synthetic-domain length along the x axis. |
100.0 m |
|
|
Synthetic-domain length along the y axis. |
10.0 m |
|
|
Grid cell count along the x axis. |
50 |
|
|
Grid cell count along the y axis. |
5 |
|
|
Synthetic topography shape used by the benchmark. |
flat |
|
|
Base land-surface elevation of the synthetic topography. |
20 m |
|
|
Depth model used to build the aquifer support. |
constant_thickness |
|
|
Aquifer or support thickness used by the benchmark. |
20.0 m |
|
|
Steady or transient flow regime used by the benchmark. |
transient |
|
|
Sink and source families activated in the benchmark. |
[recharge] |
|
|
Boundary-condition families activated in the benchmark. |
[west_side, east_side] |
|
|
Hydraulic parameter families explicitly configured by the benchmark. |
[K, Ss, Sy] |
|
|
Parameterization mode used for K. |
homogeneous |
|
|
Homogeneous K value used by the benchmark. |
1e-4 m/s |
|
|
Parameterization mode used for Ss. |
homogeneous |
|
|
Homogeneous Ss value used by the benchmark. |
1e-10 m-1 |
|
|
Parameterization mode used for Sy. |
homogeneous |
|
|
Homogeneous Sy value used by the benchmark. |
0.10 - |
|
|
Initial-condition policy used to start the benchmark. |
custom |
|
|
Scalar initial head or top offset used by the initial-condition policy. |
10.0 m |
|
|
Fixed head applied on the west side boundary. |
10.0 m |
|
|
Fixed head applied on the east side boundary. |
10.0 m |
|
|
Case-specific configuration field flow.sinks_sources.recharge.negative_to_evt used by the validation benchmark. |
true |
|
|
External data families loaded by the benchmark. |
[recharge] |
|
|
Recharge data source mode used by the benchmark. |
synthetic |
|
|
Recharge values used by the benchmark forcing. |
[5 mm/day] |
|
|
Amplitude of the periodic recharge forcing. |
5 mm/day |
|
|
Period of the periodic recharge forcing. |
10 days |
|
|
Start date of the recharge forcing. |
2003-01-01 |
|
|
Sampling frequency used for the recharge forcing. |
D |
|
|
Number of recharge forcing periods. |
40 |
|
|
Runoff ratio applied when converting recharge forcing to effective infiltration. |
0 |
|
Solver-Specific Overrides#
Field |
Meaning |
Value |
Source |
|---|---|---|---|
|
Planar support construction mode used by MODFLOW-NWT. |
resample_to_shape |
|
|
Planar support cell count along x used by MODFLOW-NWT. |
50 |
|
|
Planar support cell count along y used by MODFLOW-NWT. |
5 |
|
|
Planar support resampling mode used by MODFLOW-NWT. |
nearest |
|
|
Number of vertical layers used by MODFLOW-NWT. |
1 |
|
|
Whether the first time period is treated as steady by MODFLOW-NWT. |
false |
|
Field |
Meaning |
Value |
Source |
|---|---|---|---|
|
Solver-specific override applied to MODFLOW 6. |
false |
|
|
Linear-solver complexity preset used by MODFLOW 6. |
COMPLEX |
|
|
Planar support construction mode used by MODFLOW 6. |
resample_to_shape |
|
|
Planar support cell count along x used by MODFLOW 6. |
50 |
|
|
Planar support cell count along y used by MODFLOW 6. |
5 |
|
|
Planar support resampling mode used by MODFLOW 6. |
nearest |
|
|
Number of vertical layers used by MODFLOW 6. |
1 |
|
|
Whether the first time period is treated as steady by MODFLOW 6. |
false |
|
Field |
Meaning |
Value |
Source |
|---|---|---|---|
|
Solver-specific override applied to MODFLOW 6. |
false |
|
|
Linear-solver complexity preset used by MODFLOW 6. |
COMPLEX |
|
|
Vertical anisotropy ratio passed to MODFLOW 6. |
1 |
|
|
Number of vertical layers used by MODFLOW 6. |
1 |
|
|
Whether the first time period is treated as steady by MODFLOW 6. |
false |
|
|
Committed unstructured mesh file used by the irregular-mesh solver variant. |
../../../shared/mesh_bundles/linearized_unconfined_drainage_irregular_tri_100x10/mesh_2d.msh |
|
|
Committed mesh-bundle directory used to recover support metadata for the irregular-mesh solver variant. |
../../../shared/mesh_bundles/linearized_unconfined_drainage_irregular_tri_100x10 |
|
Field |
Meaning |
Value |
Source |
|---|---|---|---|
|
Runtime backend selected for the in-house solver. |
petsc |
|
Acceptance Criteria#
Field |
Meaning |
Value |
Source |
|---|---|---|---|
|
Simulated observable compared against the reference solution. |
watertable_elevation |
|
|
Expected number of stored time periods checked by the validation helper. |
40 |
|
|
Expected spatial shape for each stored time step. |
[5, 50] |
|
Acceptance Criteria by Solver#
Field |
Meaning |
Value |
Source |
|---|---|---|---|
|
Expected output shape or time-space layout checked for this solver. |
Expected output: 40 periods, spatial shape 5 x 50 |
|
|
Maximum accepted root-mean-square error for space time. |
0.02 |
|
|
Maximum accepted absolute error for space time. |
0.03 |
|
|
Maximum accepted cross-row spread for space time. |
0.0001 |
|
|
Maximum accepted root-mean-square error for final profile. |
0.02 |
|
|
Maximum accepted absolute error for final profile. |
0.03 |
|
Field |
Meaning |
Value |
Source |
|---|---|---|---|
|
Expected output shape or time-space layout checked for this solver. |
Expected output: 40 periods, spatial shape 5 x 50 |
|
|
Maximum accepted root-mean-square error for space time. |
0.01 |
|
|
Maximum accepted absolute error for space time. |
0.02 |
|
|
Maximum accepted cross-row spread for space time. |
1e-05 |
|
|
Maximum accepted root-mean-square error for final profile. |
0.002 |
|
|
Maximum accepted absolute error for final profile. |
0.003 |
|
Field |
Meaning |
Value |
Source |
|---|---|---|---|
|
Expected output shape or time-space layout checked for this solver. |
Expected output: 40 periods, spatial shape 5 x 50 |
|
|
Maximum accepted root-mean-square error for space time. |
0.02 |
|
|
Maximum accepted absolute error for space time. |
0.03 |
|
|
Maximum accepted cross-row spread for space time. |
0.006 |
|
|
Maximum accepted root-mean-square error for final profile. |
0.02 |
|
|
Maximum accepted absolute error for final profile. |
0.03 |
|
Field |
Meaning |
Value |
Source |
|---|---|---|---|
|
Expected output shape or time-space layout checked for this solver. |
Expected output: 40 periods, spatial shape 5 x 50 |
|
|
Maximum accepted root-mean-square error for space time. |
0.02 |
|
|
Maximum accepted absolute error for space time. |
0.03 |
|
|
Maximum accepted cross-row spread for space time. |
0.0001 |
|
|
Maximum accepted root-mean-square error for final profile. |
0.02 |
|
|
Maximum accepted absolute error for final profile. |
0.03 |
|
Source Pointers#
validation_cases/README.mdvalidation_cases/analytical/transient/linearized_unconfined_recharge_periodic_1d/README.mdvalidation_cases/analytical/transient/linearized_unconfined_recharge_periodic_1d/reference.pyvalidation_cases/analytical/transient/linearized_unconfined_recharge_periodic_1d/comparison.pyvalidation_cases/analytical/transient/linearized_unconfined_recharge_periodic_1d/plotting.pyvalidation_cases/analytical/transient/linearized_unconfined_recharge_periodic_1d/run_case.pyvalidation_cases/analytical/transient/linearized_unconfined_recharge_periodic_1d/metadata.tomlvalidation_cases/analytical/transient/linearized_unconfined_recharge_periodic_1d/config_modflownwt.tomlvalidation_cases/analytical/transient/linearized_unconfined_recharge_periodic_1d/runtime_boussinesq.pyvalidation_cases/analytical/transient/linearized_unconfined_recharge_periodic_1d/tolerances.tomlvalidation_cases/analytical/transient/linearized_unconfined_recharge_periodic_1d/tolerances_modflow6.tomlvalidation_cases/analytical/transient/linearized_unconfined_recharge_periodic_1d/tolerances_modflow6_irregular_tri.tomlvalidation_cases/analytical/transient/linearized_unconfined_recharge_periodic_1d/config_modflow6.tomlvalidation_cases/analytical/transient/linearized_unconfined_recharge_periodic_1d/config_modflow6_irregular_tri.tomlvalidation_cases/analytical/transient/linearized_unconfined_recharge_periodic_1d/config_boussinesq.tomlvalidation_cases/shared/boussinesq_uniform_strip.pyvalidation_cases/analytical/transient/linearized_unconfined_1d.py
Artifacts#
docs/source/_static/capability_gallery/validation/linearized_unconfined_recharge_periodic_1d__modflownwt.pngdocs/source/_static/capability_gallery/validation/linearized_unconfined_recharge_periodic_1d__modflow6.pngdocs/source/_static/capability_gallery/validation/linearized_unconfined_recharge_periodic_1d__modflow6_irregular_tri.pngdocs/source/_static/capability_gallery/validation/linearized_unconfined_recharge_periodic_1d__boussinesq.pngdocs/source/_static/capability_gallery/validation/linearized_unconfined_recharge_periodic_1d_summary.jsonstores the displayed metrics plus source hashes used bypython -m tools.doc_gallery --check.