User's guide of Proceessing Modflow 5.0

Processing Modflow 149
course of an estimation process, the absolute value of a parameter falls below the product
of FACORIG and its original value, then the product is substituted for the denominators
of eq. 3.55 or eq. 3.56 to prevent the denominators becoming zero or too small.
FACORIG is not used to adjust limits for log-transformed parameters. FACORIG must
be greater than zero. A value of 0.001 is often adequate.
- PHIREDSWH is a criterion for switching the calculation method of derivatives between
the forward finite difference method and the central finite difference method. If, for the
i-th iteration the relative reduction in the objective function between successive
optimization iterations is less than PHIREDSWH, PEST will switch to three-point
derivatives calculation for those parameter groups with FORCEN = Switch. The relative
reduction in the objective function is defined by [(N - N ) / N ], where N is the
i-1 i i-1 i
objective function calculated on the basis of the upgraded parameter set determined in
the i-th iteration.
A value of 0.1 is often suitable for PHIREDSWH. If it is set too high, PEST may
make the switch to three-point derivatives calculation too early. The result will be that
more model runs will be required than are really needed at that stage of the estimation
process. If PHIREDSWH is set too low, PEST may waste an optimization iteration or
two in lowering the objective function to a smaller extent than would have been possible,
if it had made an earlier switch to central derivatives calculation.
Note that PHIREDSWH should be set considerably higher than PHIREDSTP (see
below) which sets one of the termination criteria on the basis of the relative objective
function reduction between optimization iterations.
- NOPTMAX is the maximum number of optimization iterations. A value of 20 to 30 is
often adequate. 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.
- PHIREDSTP and NPHISTP are convergence criteria. For many cases 0.01 and 3 are
suitable values for PHIREDSTP and NPHISTP respectively.
If, in the course of the parameter estimation process, there have been NPHISTP
optimization iterations for which
(M i & M min )
M i
# PHIREDSTP
(3.57)
(N being the objective function value at the end of the i-th optimization iteration and N
i min
being the lowest objective function achieved to date), PEST will end the optimization
process.
3.6.5 PEST (Inverse Modeling)