Linearized Unconfined Drainage 1D#

Note

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Steady synthetic groundwater-flow case used to validate HydroModPy’s top drainage boundary condition against a closed-form linearized 1D reference with:

Case Setup#

  • Homogeneous strip, fixed west/east heads, distributed top drainage everywhere, flat drainage level

  • Available solver variants: MODFLOW-NWT, MODFLOW 6, MODFLOW 6 irregular triangles.

What It Shows#

  • validate the drainage boundary-condition path with an analytical benchmark,

  • keep drainage active everywhere so the reference stays closed-form,

  • isolate one lightweight 1D equilibrium before tackling more complex seepage-face cases.

  • drainage boundary-condition path in a controlled analytical setting

  • Primary metrics: head-profile RMSE, max abs error, cross-row spread.

  • Solver-specific figures and metrics are shown side by side so the same benchmark can be read across backends.

Analytical Reference#

  • compared quantity: domain-averaged head profile along x

  • reference: steady linearized unconfined profile with distributed top drainage

\[T_0\,\frac{\mathrm{d}^2u}{\mathrm{d}x^2}-\lambda_d\,u=0,\qquad u=h-z_d,\qquad \lambda_d=\frac{C_d}{A}\]
\[u(x)=u_w\frac{\sinh\left(\beta(L-x)\right)}{\sinh\left(\beta L\right)}+u_e\frac{\sinh\left(\beta x\right)}{\sinh\left(\beta L\right)},\qquad \beta=\sqrt{\frac{\lambda_d}{T_0}}\]

Solver Coverage#

  • Default solver: MODFLOW-NWT

  • Available variants: MODFLOW-NWT, MODFLOW 6, MODFLOW 6 irregular triangles

Linearized Unconfined Drainage 1D validation figure for MODFLOW-NWT
Linearized Unconfined Drainage 1D rendered with MODFLOW-NWT for the analytical gallery.

Metrics - Head-profile RMSE: 0.0127 m - Head-profile max abs error: 0.0175 m - Cross-row head spread: 1.91e-07 m

  • Config file: validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

  • Tolerances: validation_cases/analytical/steady/linearized_unconfined_drainage_1d/tolerances.toml

  • Expected shape: 5 x 50

python -m validation_cases.analytical.steady.linearized_unconfined_drainage_1d.run_case --no-show --solver modflow_nwt
Linearized Unconfined Drainage 1D validation figure for MODFLOW 6
Linearized Unconfined Drainage 1D rendered with MODFLOW 6 for the analytical gallery.

Metrics - Head-profile RMSE: 0.0127 m - Head-profile max abs error: 0.0175 m - Cross-row head spread: 1.59e-07 m

  • Config file: validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflow6.toml

  • Tolerances: validation_cases/analytical/steady/linearized_unconfined_drainage_1d/tolerances_modflow6.toml

  • Expected shape: 5 x 50

python -m validation_cases.analytical.steady.linearized_unconfined_drainage_1d.run_case --no-show --solver modflow6
Linearized Unconfined Drainage 1D validation figure for MODFLOW 6 irregular triangles
Linearized Unconfined Drainage 1D rendered with MODFLOW 6 irregular triangles for the analytical gallery.

Metrics - Head-profile RMSE: 0.0463 m - Head-profile max abs error: 0.0640 m - Cross-row head spread: 0.00e+00 m

  • Config file: validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflow6_irregular_tri.toml

  • Tolerances: validation_cases/analytical/steady/linearized_unconfined_drainage_1d/tolerances.toml

  • Expected shape: 5 x 50

python -m validation_cases.analytical.steady.linearized_unconfined_drainage_1d.run_case --no-show --solver modflow6_irregular_tri

Reproduce#

Run the underlying example or validation case with:

python -m validation_cases.analytical.steady.linearized_unconfined_drainage_1d.run_case --no-show

Refresh the committed gallery artifacts with:

python -m tools.doc_gallery

Case Parameters#

Reference Parameters#

Field

Meaning

Value

Source

xmin

Minimum x coordinate of the analytical reference domain.

0

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/metadata.toml

xmax

Maximum x coordinate of the analytical reference domain.

100

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/metadata.toml

length_y_m

Reference-domain length along the y axis.

10 m

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/metadata.toml

west_head_m

Fixed west-boundary hydraulic head used by the reference solution.

6.2 m

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/metadata.toml

east_head_m

Fixed east-boundary hydraulic head used by the reference solution.

5.8 m

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/metadata.toml

drainage_elevation_m

Drainage elevation used by the analytical drainage reference.

0 m

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/metadata.toml

drainage_conductance_m2_per_s

Drainage conductance used by the analytical drainage boundary.

1e-07 m2/s

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/metadata.toml

hydraulic_conductivity_m_per_s

Hydraulic conductivity used by the analytical or benchmark reference.

0.0001 m/s

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/metadata.toml

reference_saturated_thickness_m

Reference saturated thickness used by the linearized formulation.

26 m

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/metadata.toml

aquifer_thickness_m

Aquifer thickness used by the reference formulation.

20 m

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/metadata.toml

profile_axis

Axis along which the validation profile is extracted.

0

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/metadata.toml

Common Numerical Setup#

Field

Meaning

Value

Source

workflow

Case-specific configuration field workflow used by the validation benchmark.

simulation

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

geographic.synthetic.grid.length_x

Synthetic-domain length along the x axis.

100.0 m

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

geographic.synthetic.grid.length_y

Synthetic-domain length along the y axis.

10.0 m

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

geographic.synthetic.grid.nx

Grid cell count along the x axis.

50

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

geographic.synthetic.grid.ny

Grid cell count along the y axis.

5

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

geographic.synthetic.topography.kind

Synthetic topography shape used by the benchmark.

flat

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

geographic.synthetic.topography.base_elevation

Base land-surface elevation of the synthetic topography.

0 m

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

domain.depth_model.type

Depth model used to build the aquifer support.

constant_thickness

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

domain.depth_model.thickness

Aquifer or support thickness used by the benchmark.

20.0 m

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

flow.flow_regime

Steady or transient flow regime used by the benchmark.

steady

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

flow.active_sinks_sources

Sink and source families activated in the benchmark.

[]

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

flow.active_bc

Boundary-condition families activated in the benchmark.

[west_side, east_side, drainage]

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

flow.param_list

Hydraulic parameter families explicitly configured by the benchmark.

[K]

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

flow.param.K.field.kind

Parameterization mode used for K.

homogeneous

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

flow.param.K.field.value

Homogeneous K value used by the benchmark.

1e-4 m/s

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

flow.ic.type

Initial-condition policy used to start the benchmark.

custom

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

flow.ic.value

Scalar initial head or top offset used by the initial-condition policy.

6.0 m

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

flow.bc.dirichlet.west_side.value

Fixed head applied on the west side boundary.

6.2 m

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

flow.bc.dirichlet.east_side.value

Fixed head applied on the east side boundary.

5.8 m

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

flow.bc.cauchy.drainage.application_domain

Part of the domain where the drainage Cauchy boundary is applied.

top

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

flow.bc.cauchy.drainage.value

Cauchy coefficient or conductance applied on the drainage boundary.

1e-7 m2/s

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

Solver-Specific Overrides#

Field

Meaning

Value

Source

modflownwt.sgrid.planar.mode

Planar support construction mode used by MODFLOW-NWT.

resample_to_shape

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

modflownwt.sgrid.planar.nx

Planar support cell count along x used by MODFLOW-NWT.

50

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

modflownwt.sgrid.planar.ny

Planar support cell count along y used by MODFLOW-NWT.

5

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

modflownwt.sgrid.planar.resampling

Planar support resampling mode used by MODFLOW-NWT.

nearest

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

modflownwt.sgrid.vertical.nlay

Number of vertical layers used by MODFLOW-NWT.

1

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

Field

Meaning

Value

Source

modflow6.runtime.mf_verbose

Solver-specific override applied to MODFLOW 6.

false

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflow6.toml

modflow6.runtime.mf6_ims_complexity

Linear-solver complexity preset used by MODFLOW 6.

COMPLEX

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflow6.toml

modflow6.sgrid.planar.mode

Planar support construction mode used by MODFLOW 6.

resample_to_shape

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflow6.toml

modflow6.sgrid.planar.nx

Planar support cell count along x used by MODFLOW 6.

50

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflow6.toml

modflow6.sgrid.planar.ny

Planar support cell count along y used by MODFLOW 6.

5

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflow6.toml

modflow6.sgrid.planar.resampling

Planar support resampling mode used by MODFLOW 6.

nearest

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflow6.toml

modflow6.sgrid.vertical.nlay

Number of vertical layers used by MODFLOW 6.

1

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflow6.toml

Field

Meaning

Value

Source

modflow6.runtime.mf_verbose

Solver-specific override applied to MODFLOW 6.

false

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflow6_irregular_tri.toml

modflow6.runtime.mf6_ims_complexity

Linear-solver complexity preset used by MODFLOW 6.

COMPLEX

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflow6_irregular_tri.toml

modflow6.process_specific.vka

Vertical anisotropy ratio passed to MODFLOW 6.

1

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflow6_irregular_tri.toml

modflow6.sgrid.vertical.nlay

Number of vertical layers used by MODFLOW 6.

1

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflow6_irregular_tri.toml

mesh_input.mesh_path

Committed unstructured mesh file used by the irregular-mesh solver variant.

../../../shared/mesh_bundles/linearized_unconfined_drainage_irregular_tri_100x10/mesh_2d.msh

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflow6_irregular_tri.toml

mesh_input.bundle_dir

Committed mesh-bundle directory used to recover support metadata for the irregular-mesh solver variant.

../../../shared/mesh_bundles/linearized_unconfined_drainage_irregular_tri_100x10

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflow6_irregular_tri.toml

Acceptance Criteria#

Field

Meaning

Value

Source

output.observable_name

Simulated observable compared against the reference solution.

watertable_elevation

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/metadata.toml

output.expected_shape

Expected spatial output shape checked by the validation helper.

[5, 50]

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/metadata.toml

Acceptance Criteria by Solver#

Field

Meaning

Value

Source

expected_output

Expected output shape or time-space layout checked for this solver.

Expected shape: 5 x 50

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/metadata.toml

head_profile.rmse

Maximum accepted root-mean-square error for head profile.

0.05

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/tolerances.toml

head_profile.max_abs_error

Maximum accepted absolute error for head profile.

0.1

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/tolerances.toml

head_profile.row_spread

Maximum accepted cross-row spread for head profile.

2e-05

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/tolerances.toml

Field

Meaning

Value

Source

expected_output

Expected output shape or time-space layout checked for this solver.

Expected shape: 5 x 50

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/metadata.toml

head_profile.rmse

Maximum accepted root-mean-square error for head profile.

0.015

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/tolerances_modflow6.toml

head_profile.max_abs_error

Maximum accepted absolute error for head profile.

0.02

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/tolerances_modflow6.toml

head_profile.row_spread

Maximum accepted cross-row spread for head profile.

5e-06

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/tolerances_modflow6.toml

Field

Meaning

Value

Source

expected_output

Expected output shape or time-space layout checked for this solver.

Expected shape: 5 x 50

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/metadata.toml

head_profile.rmse

Maximum accepted root-mean-square error for head profile.

0.05

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/tolerances.toml

head_profile.max_abs_error

Maximum accepted absolute error for head profile.

0.1

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/tolerances.toml

head_profile.row_spread

Maximum accepted cross-row spread for head profile.

2e-05

validation_cases/analytical/steady/linearized_unconfined_drainage_1d/tolerances.toml

Source Pointers#

  • validation_cases/README.md

  • validation_cases/analytical/steady/linearized_unconfined_drainage_1d/README.md

  • validation_cases/analytical/steady/linearized_unconfined_drainage_1d/reference.py

  • validation_cases/analytical/steady/linearized_unconfined_drainage_1d/comparison.py

  • validation_cases/analytical/steady/linearized_unconfined_drainage_1d/plotting.py

  • validation_cases/analytical/steady/linearized_unconfined_drainage_1d/run_case.py

  • validation_cases/analytical/steady/linearized_unconfined_drainage_1d/metadata.toml

  • validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflownwt.toml

  • validation_cases/analytical/steady/linearized_unconfined_drainage_1d/tolerances.toml

  • validation_cases/analytical/steady/linearized_unconfined_drainage_1d/tolerances_modflow6.toml

  • validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflow6.toml

  • validation_cases/analytical/steady/linearized_unconfined_drainage_1d/config_modflow6_irregular_tri.toml

  • validation_cases/analytical/transient/linearized_unconfined_1d.py

Artifacts#

  • docs/source/_static/capability_gallery/validation/linearized_unconfined_drainage_1d__modflownwt.png

  • docs/source/_static/capability_gallery/validation/linearized_unconfined_drainage_1d__modflow6.png

  • docs/source/_static/capability_gallery/validation/linearized_unconfined_drainage_1d__modflow6_irregular_tri.png

  • docs/source/_static/capability_gallery/validation/linearized_unconfined_drainage_1d_summary.json stores the displayed metrics plus source hashes used by python -m tools.doc_gallery --check.