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iMOD User Manual version 5.2 (html)


10.15Data Set 14: Parameter Estimation – Main settings

Data Set 14

PE_MXITER,PE_STOP,PE_SENS,PE_NPERIOD,PE_NBATCH, PE_TARGET_H,PE_TARGET_D,PE_SCALING,PE_PADJ,PE_DRES,
PE_KTYPE,PE_KRANGE,
PE_REGULARISATION,PE_REGFACTOR

PE_MXITER

MXITER can have different meanings:

\(<\)0

iMODFLOW will be run a single run and adjust all parameters accordingly and than stop.

=0

If PE_MXITER is equal to zero, a sensitivity matrix will be computed yielding Jacobian values (finite difference between the change in head and the parameter update) for the entire zones. Those values will be written to disk in .\head\head_{date}_l{i}_sens_{param}_ils{ils}.idf. Those values can be helpful to estimate the adjustment to a parameter to yield a desired improvement of the head and/or flux (assuming the model act linearly). The process will stop whenever all parameters are perturbed.

\(>\)0

Maximum number of iterations.

PE_STOP

Stop criterion whenever decrease of objective function J becomes less or equal to the ratio J\({}_{i}\)/J\({}_{i}\)\({}_{-1}\). Entering a value of 0.1 means than the optimization stops whenever the objective function value J\({}_{i}\) for the current optimization step i, is reduced less than 10% of the last objective function value J\({}_{i-1}\).

PE_SENS

Enter the acceptable sensitivity for parameters to be included in the parameter upgrade vector, e.g. PE_SENS=0.5 mean that parameters that have less than 0.5% sensitivity will be left out until they achieve a higher sensitivity.

PE_NPERIOD

Enter the number of periods. If PE_NPERIOD \(>\) 0, than repeat Data Set 15 for each period.

PE_NBATCH

Enter the number of batch files to be included during the parameter estimation. Each batch file can have its own fraction that determines the weigh for the total objective function value.

PE_TARGET_H
PE_TARGET_D

Enter a fraction for each target, PE_TARGET_H is the error for the head differences, PE_TARGET_D, the error for the dynamics differences (differences to its average value). Both need to be specified with a fraction (summed to be 1.0) to express the ratio in which both are used in the weighting of the total objective function. E.g. PE_TARGET_H=0.80 and PE_TARGET_D=0.20, denotes that the head differences determime the objective function value for 80%, as the dynamics differences take into account 20%. The entered fraction should be entered relative to each other since iMODFLOW will recomputed the normalized values for the fraction. e.g. entering 1.0 and 2.0 will yield the fraction values 0.33 and 0.66, they will be summed equal to one. Whenever PE_NBATCH\(>\)0 (see Data Set 16), the entered weigh values for each batch file will be included in the final normalization of the fractions.

PE_SCALING

Enter a scaling option:

0

No use of scaling/Eigenvalue decomposition (SVD)

1

Only use of scaling

2

Use of scaling and Eigenvalue decomposition (SVD)

3

Only use of Eigenvalue decomposition (SVD)

In case a SVD decomposition is used (PE_SCALING=2 and PE_SCALING=3), eigenvalues that explain at least 99% of variance are included.

PE_PADJ

Enter the stopping criteria for Parameter ADJustment, e.g. PE_PADJ=0.05 means than whenever the parameter adjustment vector is less than 0.05, the optimization will stop. By default PE_PADJ=0.0 which means that the optimization will stop only whenever to parameters adjustment is applied.

PE_DRES

Enter the minimal acceptable absolute residual used for the objective function. Absolute residuals smaller that PE_DRES will not be included in the objective function and therefore not influence any parameter adjustment. By default PE_DRES=0.0 which means that all residuals will be included. Whenever PE_DRES=0.0 it represents that all differences are taken into account OR, the specified column number is used per measurement separately.

PE_KTYPE

Enter the type of Kriging to be used (whenever the PilotPoint concept is used). Apply a negative number for PE_KTYPE to use a zone for the kriging, see PPBNDIDF in Dataset 17.

-1 or 1

By default Simple Kriging is applied (PE_KTYPE=1);

-2 or 2

Select PE_KTYPE=2 for Ordinary Kriging. The latter is used whenever a trend exists in the PilotPoints.

PE_KRANGE

Enter the size of the range (meter) which is used whenever pilot points are used, e.g. PE_KRANGE=5000.0. If PE_KRANGE=0.0, the range is determined as 90% of the diagonal of the model dimensions.

PE_REGULARI-
SATION

Enter PE_REGULARISATION=1 to apply a regularisation for the prior-estimated parameter values. Any deviation of the prior-estimated parameter value will punish the objective function quadratic as \(\sigma ^{-2}(p_{\rm ini}-p)^2\). The standard deviaton \(\sigma \) is determined as the \(\sigma =4^{-1}(\log 10{PMAX}-\log 10{PMIN})\)