GMS:PEST ASP Package
When performing automated parameter estimation, a set of optimal parameter values can only be found if MODFLOW produces a stable solution for all iterations. One of the things that can cause problems with the inverse model is cells going dry. The dry cell flag that is written to the head array can cause instability in the inverse model, and thus it will not converge. When such problems occur, a successful run may be achieved by turning on some convergence options that have been added to the GMS version of MODFLOW by John Doherty. The PEST-ASP package is available in MODFLOW-2000, -2005, -NWT, and -LGR, but not in MODFLOW-USG (which uses an entirely different discretization). Once the package is selected in the MODFLOW Packages/Processes dialog the PEST ASP options are accessed via the PEST ASP Package (Advanced Spatial Parameterization) command in the MODFLOW | Optional Packages menu. The options are as follows:
Do Not Stop on Non-Convergence
The Do not stop ... option is used for transient simulations. When this option is on, if the MODFLOW model does not converge for a particular time step, it continues to the next time step rather than aborting.
Assign Bottom Elevation to Dry Cells
During a normal MODFLOW run, if a cell goes dry, the HDRY value assigned in the BCF package is assigned to the cell. The default value for HDRY is -888. At each iteration of the inverse model run (each time a MODFLOW solution is found), the inverse model interpolates the computed head values to the observation points and computes the residual error. This error is factored into the objective function. If the head at a cell near an observation point suddenly switches from a normal head value to -888, an extreme discontinuity is introduced to the objective function and the inverse model may not be able to converge. This problem can be avoided by turning on the Assign bottom elevation to dry cells option. If this option is on, the bottom elevation associated with the cell is assigned as the head value for the cell.
Prevent Cell Drying
The Prevent Cell Drying option does not allow a cell in the bottom layer to go dry. The head is not allowed to drop below the value corresponding to the specified minimum saturated thickness. Additional instruction is provided by Richard Winston and in a USGS Open-File:
- Use of the wetting capability can cause serious problems with convergence. There are several methods to avoid this.
- If a cell should never become wet, make it an inactive cell rather than a variable head cell.
- Adjust the value of the wetting threshold in WETDRY. (Higher is more stable but may be less accurate.)
- Decide which neighbors will be checked to decide if a cell should be wetted using WETDRY. Often it is better to allow only the cell beneath the dry cell to rewet it.
- Use IHDWET to determine which equation is used to specify the head in newly wetted cells.
- Can vary the wetting factor WETFCT.
- In steady-state conditions, adjust initial conditions to values that are close to the user's best guess of the final conditions to improve stability.
- Choose a different solver. The SIP, PCG1, and PCG2 solvers will work with the wetting capability. The SOR solver doesn't work well with the wetting capability. Note that cells can not change between wet and dry during the inner iterations of the PCG1 and PCG2 solvers. The PCG1 solver is no longer included in the USGS version of MODFLOW.
- When using the PCG2 solver, set RELAX in the range of 0.97 to 0.99 to avoid zero divide and non-diagonally dominant matrix errors. (However, this is an infrequent cause of instability. If such an error occurs, PCG2 prints an error message in the output file and aborts the simulation.)
- When using the PCG2 solver, set DAMP to a value between 0 and 1.
- Unrealistically high conductances on boundary cells can contribute to instability. Check the conductances in the Drain, River, Reservoir, Lake, Stream, and General-Head Boundary packages. In the Evapotranspiration check the EVT Flux Stress[i] and EVT Extinction Depth which together control the conductance of evapotranspiration cells.
- The two most important variables that affect stability are the wetting threshold and which neighboring cells are checked to determine if a cell should be wetted. Both of these are controlled through WETDRY. It is often useful to look at the output file and identify cells that convert repeatedly from wet to dry. Try raising the wetting threshold for those cells. It may also be worthwhile looking at the boundary conditions associated with dry cells.
- Sometimes cells will go dry in a way that will completely block flow to a sink or from a source. After that happens, the results are unlikely to be correct. It's always a good idea to look at the flow pattern around cells that have gone dry to see whether the results are reasonable.
GMS – Groundwater Modeling System
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