Define boundary conditions
Set recharge, coastal head, canal stage, and pumping terms for the scenario domain.
Numerical workflow
From boundary conditions to aquifer response
Halocline exposes each modeling step: boundary conditions are parameterized, the hydraulic head field is solved, interface position is estimated, and well-level intrusion risk is reported with diagnostics.
Solve hydraulic head field
Solve the steady-state Darcy flow field over the active grid and retain mass-balance diagnostics.
Compute interface depth
Use the Ghyben-Herzberg approximation to convert freshwater head into a sharp-interface depth estimate.
Evaluate well intrusion risk
Estimate critical pumping and risk ratio for each placeholder wellfield under the solved head field.
Attach assumptions and diagnostics
Report convergence status, mass-balance residual, active guardrails, and non-regulatory model limitations.
Boundary model
A simplified coastal-aquifer model with visible boundary assumptions
The current model represents a two-dimensional active grid, fixed-head coastal and canal boundaries, distributed recharge, pumping wells, and a provisional aquifer-base clamp used for display.
Steady flow solve
Solves the two-dimensional steady-state Darcy flow equation over the active model grid.
solver unit
m / day
Interface depth
Converts freshwater head to a sharp-interface estimate using the Ghyben-Herzberg approximation.
readout
depth m
Intrusion risk
Computes well-level pumping stress, critical pumping, and risk ratio for each placeholder wellfield.
ranking
risk ratio
Scenario parameterization
Scenario parameterization and spatial outputs
Inputs combine scalar controls and spatial fields: recharge multiplier, coastal head, canal stages, well pumping, hydraulic conductivity, fixed-head masks, and active-cell geometry. Outputs are gridded head, estimated interface depth, scenario-baseline differences, and derived well risk metrics.
Inspect live map
Biscayne / Miami-Dade
scenario inputs and output grids
Evidence posture
Model outputs are interpretable because assumptions remain visible
The interface keeps source provenance, numerical diagnostics, warning conditions, and non-regulatory model status adjacent to the modeled outputs.
Source attribution
Reference layers identify agency source, access path, transformation, and Stage 1 limitations.
Assumption readouts
Controls expose recharge, pumping, canal stage, coastal head, and tuning values instead of hiding them behind a score.
Uncertainty language
Warnings and diagnostics distinguish model guardrails from observed field conditions and future calibration work.
Why the research track exists
Coastal-aquifer calibration requires more model evaluations than manual scenario testing can support
Stage 1 keeps the calculation chain inspectable, but operational groundwater management eventually requires repeated high-fidelity calibration and uncertainty runs. The research track uses surrogate models to screen candidate scenarios before committing compute time to MODFLOW, SEAWAT, or PFLOTRAN-class simulators.
The management problem
MODFLOW-family, SEAWAT, SUTRA, and PFLOTRAN-style workflows can represent subsurface physics more completely, but calibration, uncertainty quantification, and operational scenario sweeps require many repeated forward runs. Surrogates are useful only if they reduce that search space while preserving enough spatial structure to select the correct high-fidelity runs.
GeoFUSE benchmark
360,000x
reported speedup from PFLOTRAN-scale runs to U-FNO inference
GeoFUSE training base
1,500
geological realizations used for U-FNO training
Our current test
4k / 500 / 500
synthetic oracle train, validation, and held-out test split
Target operating model
days
use surrogates to identify the right expensive runs, not replace validation
Research lineage
GeoFUSE establishes the surrogate-model precedent for seawater intrusion
GeoFUSE pairs PFLOTRAN-generated seawater-intrusion simulations with U-FNO inference, PCA parameterization, and ESMDA data assimilation. Halocline uses that result as the research baseline while testing whether WNO and GNN methods can better preserve spatial heterogeneity.
GeoFUSE
Jiang, Liu, and Dwivedi integrate U-FNO, PCA, and ESMDA for seawater intrusion prediction and uncertainty reduction on a Beaver Creek cross-section.
arXiv 2410.20118U-FNO / FNO
The Fourier neural operator lineage supplies the fast operator approximation. GeoFUSE uses U-FNO, based on Wen et al. and Li et al., to estimate pressure and salinity fields.
Wen et al. 2022WNO / GNN path
WNO brings localized multiresolution operators; graph-network surrogates bring mesh and connectivity awareness for wells, canals, faults, and irregular geology.
WNO reference
Werner et al. 2013 seawater intrusion review
Ketabchi et al. 2016 sea-level-rise review
Langevin and Guo 2006; SEAWAT 2008
Provost and Voss 2019 SUTRA
Hammond et al. 2014 PFLOTRAN
Yabusaki et al. 2020 Beaver Creek
Emerick and Reynolds 2013 ESMDA
Arora et al. 2011 / 2012 inverse estimation
Bhattacharjya and Datta 2009 ANN-GA
Sreekanth and Datta 2010 surrogate management
Hussain et al. 2015 simulation optimization
Rajabi and Ketabchi 2017 Gaussian emulation
Mo et al. 2019 deep autoregressive groundwater
Tang et al. 2020 dynamic subsurface surrogate
Li et al. 2020 Fourier neural operator
Wen et al. 2022 U-FNO multiphase flow
Meray et al. 2024 groundwater contamination surrogate
Cao et al. 2024 coastal-aquifer data assimilation
Han et al. 2024 CO2 storage surrogate
Jiang and Durlofsky 2023 multifidelity surrogates
Jiang and Durlofsky 2024 data-space inversion
Goebel et al. 2017 resistivity intrusion imaging
Dodangeh et al. 2022 joint coastal aquifer inversion
Yoon et al. 2017 saline aquifer pressure data
Zhou et al. 2022 simultaneous property inference
Zhou and Tartakovsky 2021 NN-surrogate MCMC
Sonnenborg et al. 2015 geology uncertainty
He et al. 2015 hydrological predictive uncertainty
Ebong et al. 2020 stochastic petrophysical modeling
Messier et al. 2015 groundwater radon estimation
Remy et al. 2009 SGeMS geostatistics
Siler et al. 2019 3D geothermal geology
Torresan et al. 2020 3D hydrogeology
Strati et al. 2017 integrated 3D crust model
Dwivedi et al. 2018 riparian hot moments
Zhong et al. 2019 cDC-GAN plume prediction
Kingma and Ba 2014 Adam optimizer
Current Halocline study
The current U-FNO experiment is trained on synthetic physics-oracle data
This was a compute and workflow test, not a MODFLOW/SEAWAT replacement and not a field-validated aquifer model. We rented GPU compute, generated synthetic oracle data from the Python Stage 1 solver, trained a U-FNO-style surrogate, and measured held-out error and inference speed.
Generated data
Latin Hypercube samples varied recharge, sea-level rise, three placeholder well pumpings, eleven canal stages, and five calibration-lite tuning controls. Each sample was solved by the Python oracle and stored as HDF5.
Split4,000 train / 500 val / 500 test
Grid37 x 21 active-mask domain
Grid inputsmask, x, y, K, recharge, pumping, fixed head, fixed-head mask
Extra inputs7 scalar controls + well pumping + canal stages
Targetshead grid + interface-depth grid
Careful framing
Accuracy is measured against a simplified synthetic oracle, not observations. The oracle is a 2D steady sharp-interface model, not a calibrated MODFLOW, SEAWAT, or PFLOTRAN model. The surrogate accelerates this simplified oracle; it does not replace high-fidelity numerical simulation or site calibration.
U-FNO prediction vs synthetic physics oracle
held-out test set
U-FNO prediction vs synthetic physics oracle (held-out test set). Summary metrics: head MAE 1.78 m, interface-depth MAE 8.02 m, batch-2048 inference speedup 174.57x versus the Python oracle.
Research direction
Use surrogate speed where it helps, then spend simulator time where it matters
The next step is to test surrogate architectures that preserve spatial structure in high- and low-variance geologic zones, then use that speed to choose better MODFLOW, SEAWAT, or PFLOTRAN calibration runs.
Local frequency fit
Wavelet neural operators are attractive because wavelets can localize information across space and scale. That is the right failure mode to test when Fourier-style surrogates risk blurring sharp salinity fronts or high-variance hydraulic properties.
Geometry and connectivity
Graph surrogates can represent irregular cells, wells, canal links, boundaries, and local neighborhoods more naturally than a rectangular image alone. That matters as Halocline moves from Stage 1 grids toward utility and consultant model domains.
Run the expensive model on the right cases
The practical target is a workflow where surrogate sweeps narrow thousands of candidates to the small set of scenarios and calibration runs that deserve full simulator time, shortening delivery from open-ended compute cycles to days or a week.
Working draft
Inspect the Stage 1 model and the surrogate-research path
The current product exposes the Stage 1 scenario calculation chain. The research track evaluates whether surrogate models can reduce the number of expensive simulator runs required for calibration and uncertainty analysis.