Request for Assistance with PEST++ Identifiability and Parameter Bound Issues in MODFLOW Calibration

[DEEPAK KUMAR]

Dear MODFLOW/PEST++ User Group,

I am calibrating a two-layer MODFLOW-2005 groundwater-flow model using PEST++-GLM and would appreciate assistance with a parameter identifiability and bound-convergence problem.

The model has 2 layers, 100 × 100 cells, 7 stress periods, and 51 groundwater-head observations. I am simultaneously calibrating HK, VK, and recharge using 11 adjustable parameters: HK for both layers, VK for both layers, and recharge multipliers for all 7 stress periods.

The calibration completes, but the final parameter estimates are almost entirely at their specified bounds:

• HK L1 = 0.5 × base; HK L2 = 0.5 × base — lower bounds

• VK L1 = 0.5 × base; VK L2 = 0.5 × base — lower bounds

• RCH SP1 = 75 × base; SP2 = 75 × base; SP7 = 75 × base — upper bounds

• RCH SP3–SP6 = 0.5 × base — lower bounds

PEST++ also reports:

"SVDSolver::test_upgrade_to_find_freeze_pars(): all parameters at/near bounds and heading out - cannot continue."

The weighted Jacobian is 51 × 11 with an effective rank of 11, but the parameter collinearity is extremely high:

• HK L1–HK L2 = 0.99906

• VK L1–VK L2 = 0.99541

• HK L1–RCH SP2 = 0.99724

• HK L2–RCH SP2 = 0.99752

• VK L1–RCH SP1 = 0.96661

• VK L1–RCH SP2 = 0.95764

• HK L2–VK L1 = 0.95280

The final head statistics are:

R² = 0.782, Pearson r = 0.884, RMSE = 11.77 m, MAE = 10.10 m, NSE = 0.390, and PBIAS = −1.18%.

Although the model reproduces the observed head pattern reasonably well, the regression slope is only 0.502, and the strong parameter correlations and bound solutions make me concerned that HK, VK, and recharge are compensating for one another rather than being uniquely identified.

I would particularly appreciate advice on:

1. Whether I should reduce or tie the HK/VK parameters between layers.

2. Whether using seven independent recharge multipliers is excessive for 51 head observations.

3. How to use the Jacobian, SVD, sensitivity, and parameter-correlation diagnostics to decide which parameters should be fixed, tied, or re-parameterized.

4. Whether the appropriate solution is to change parameter bounds, reduce parameters, or modify PEST++-GLM settings rather than simply widening the bounds.

I would also be very grateful if anyone could recommend or share study materials, technical documentation, tutorials, example PEST++ control files, or published studies that could help me better understand parameter identifiability, SVD analysis, parameterization, and bound-related problems in groundwater-model calibration.

 I can provide the PEST control file, parameter definitions, Jacobian/SVD diagnostics, model files, and calibration code if needed.

Thank you for your time and assistance.

Best regards,
Deepak Kumar
PhD Research Scholar
IIT (ISM) Dhanbad, India

[Richard Winston]

You need some other type of observation besides head observation to simultaneously estimate hydraulic conductivity and recharge. With only head observations, the best you can do is to estimate the ratio of recharge to hydraulic conductivity.

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This group was created in 2004 by Mr. C. P. Kumar, Former Scientist 'G', National Institute of Hydrology, Roorkee. Please visit his webpage at https://cpkumar.neocities.org/
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[Mostafa Gomaa Daoud]

Another trial is to try to expand the parameter bounds and increase the number of realisations

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