The Parameter Estimation dialog is divided up into two sections and allows the editing of inverse modeling options that are specific to two of these codes - PEST and MODFLOW PES. This dialog is available when Parameter Estimation is chosen from the Run Options in the Global Options\Basic Package dialog.
These options apply to the MF2K tab and are used with the MODFLOW PES process.
This is the maximum number of parameter estimation iterations. If this value is 0, MODFLOW calculates the variance-covariance matrix on parameters and related statistics using the starting values from the sensitivity process input file, and parameter estimation stops after one iteration.
This commonly equals 2.0, but can be less if parameter values are unstable during parameter estimation iterations.
This value is the parameter estimation closure criterion as a fractional change in parameter values. Although the default value is 0.01, larger values are often used during preliminary calibration efforts. Values as small as 0.001 may be used for theoretical work.
If this value is not 0.0, parameter estimation will converge if the least-squares objective function does not decrease by more than this value (as a percent) over two parameter estimation iterations. The default value is 0.0, but typical non-zero values are 0.01 and 0.05. See MODFLOW documentation for more explanation.
In rare cases, this can speed up the parameter estimation process.
The following options are found in the PEST tab and are used when PEST has been chosen as the inverse modeling code.
This value (NOPTMAX) sets the maximum number of optimisation iterations that PEST is permitted to undertake on a particular parameter estimation run. If you want to ensure that PEST termination is triggered by other criteria, more indicative of parameter convergence to an optimal set or of the futility of further processing, you should set this variable very high. A value of 20 to 30 is often appropriate.
If NOPTMAX is set to 0, PEST will not calculate the Jacobian matrix. Instead it will terminate execution after just one model run. This setting can thus be used when you wish to calculate the objective function corresponding to a particular parameter set and/or to inspect observation residuals corresponding to that parameter set.
If NOPTMAX is set to –1, PEST will terminate execution immediately after it has calculated the Jacobian matrix for the first time. The parameter covariance, correlation coefficient and eigenvector matrices will be written to the run record file, and parameter sensitivities will be written to the sensitivity file; these are based on the initial parameter set supplied in the PEST control file.
The relative convergence limit (PHIREDSTP) is a real variable whereas the Max # of Relative Convergence Iterations (NPHISTP) is an integer variable. If, in the course of the parameter estimation process, there have been NPHISTP optimisation iterations for which
(Φi - Φmin )/Φi ≤ PHIREDSTP (4.6)
(Φi being the objective function value at the end of the i’th optimisation iteration and Φmin being the lowest objective function achieved to date), PEST will consider that the optimisation process is at an end.
For many cases 0.01 and 4 are suitable values for PHIREDSTP and NPHISTP respectively. However you must be careful not to set NPHISTP too low if the optimal values for some parameters are near or at their upper or lower bounds. In this case it is possible that the magnitude of the parameter upgrade vector may be curtailed over one or a number of optimisation iterations to ensure that no parameter value overshoots its bound. The result may be smaller reductions in the objective function than would otherwise occur.
If the magnitude of the maximum relative parameter change between optimisation iterations is less than the Relative Parameter Change Criterion (RELPARSTP) over Max # of Relative Parameter Change Iterations (NRELPAR) successive iterations, PEST will cease execution.
All adjustable parameters, whether they are relative-limited or factor-limited, are involved in the calculation of the maximum relative parameter change. RELPARSTP is a real variable for which a value of 0.01 is often suitable. NRELPAR is an integer variable; a value of 2 or 3 is normally satisfactory.
This (RELPARMAX) is the maximum relative change that a parameter is allowed to undergo between optimisation iterations.
This (FACPARMAX) is the maximum factor change that a parameter is allowed to undergo during an iteration.
If this option is chosen, PEST will use the derivatives calculated by the MODFLOW SEN process to populate the jacobian matrix. Using this option will decrease the computation time, but in some cases this can be the less robust option.
Select these options if you want these arrays written to external files. These arrays will also be written to the PEST output file (*.rec).
This is the upper limit of the measurement objective function (ie. the upper level of model-to-measurement misfit) that is tolerable when trying to minimise the regularisation objective function Φr.
This is the acceptable level for the measurement objective function that PEST uses to change its method of calculating the Marquardt Lamdas (see PEST documentation).
Normally PHIMACCEPT should be about 5% to 10% greater than PHIMLIM. However if PEST is performing well, you may wish to make it closer to PHIMLIM than this. In choosing the best parameter set at any stage of the optimisation process (for recording in the parameter value file) PEST looks at all parameter sets for which it has carried out model runs up to that point in the process. If any of these runs have resulted in an objective function less than PHIMACCEPT, it then searches from among these runs for the parameter set which gave rise to the lowest regularisation objective function. If PHIMACCEPT is set too close to PHIMLIM, PEST’s selection of the best parameter set may be restricted somewhat, for there may be some parameter sets for which the measurement objective function Φm is just above PHIMACCEPT but for which Φr is quite low. Alternatively, if PHIMACCEPT is set too large, then PEST might not try hard enough to reduce Φm to Φmi, preferring instead to work within the weaker constraint set by PHIMACCEPT. When working in regularisation mode, PEST prints out Φr and Φm for every parameter upgrade attempt. It will be apparent from this information whether PHIMACCEPT has been set correctly.
PEST ignores the value supplied for FRACPHIM unless it is greater than zero. A value of between zero and 1.0 (but normally less than about 0.3) can be supplied for this variable if you are unsure what value to use for PHIMLIM. See the PEST documentation.
This is used to change the weight applied to each pilot point.
This is an option provided by PEST that can result in a better model fit, but it may require a significant amount of computational time. See the PEST documentation for more information.
Related Links:
MODFLOW Run Options