User's guide of Proceessing Modflow 5.0

146 Processing Modflow
PIVAL and WEIGHT. The former is the value of the right side of the prior information
equation. The latter is the weight pertaining to the article of prior information in the
parameter estimation process. The weight should be inversely proportional to the standard
deviation of the prior information value (PIVAL); it can be zero if you wish, but not be
negative. The following lines show some examples, refer to Doherty et al. (1994) for more
details on the prior information. In PMWIN, the parameter name of the first parameter is P1.
The parameter name of the second parameter is P2 and so on.
1.0 * log(P1) + 1.2 * log(P2) = -5.6 1.0
1.0 * P1 + 1.455 * P2 - 3.98 * P3 + 2.123 * P4 = 1.03E-3 2.00
2.12 * P3 + 3.2 * P6 = 1.344 2.20
< Control Data
The control data are used to set internal array dimensions of PEST and tune the
optimization algorithm to the problem at hand. The items of the control data are described
in details below. When in doubt, you should use the default values given by PMWIN.
- RLAMBDA1 is the initial Marquardt lambda. PEST attempts parameter improvement
using a number of different Marquardt lambdas during any one optimization iteration. In
the course of the overall parameter estimation process, the Marquardt lambda generally
gets smaller. An initial value of 1.0 to 10.0 is appropriate for many models, though if
PEST complains that the normal matrix is not positive definite, you will need to provide
a higher initial Marquardt lambda. For high values of the Marquardt parameter (and
hence of the Marquardt lambda) the parameter estimation process approximates the
gradient method of optimization. While the latter method is inefficient and slow if used
for the entire optimization process, it often helps in getting the process started, especially
if initial parameter estimates are poor. PEST reduces lambda if it can. However if the
normal matrix is not positive definite or if a reduction in lambda does not lower the
objective function, PEST has no choice but to increase lambda.
- RLAMFAC is the factor by which the Marquardt lambda is adjusted. RLAMFAC must
be greater than 1.0. When PEST reduces lambda it divides by RLAMFAC; when it
increases lambda it multiplies by RLAMFAC.
- PHIRATSUF is the first criterion for moving to the next optimization iteration. During
any one optimization iteration, PEST tries lots of parameter sets and will consider that
the goal of the iteration has been achieved if
M i
M i&1
# PHIRATSUF
3.6.5 PEST (Inverse Modeling)
(3.53)