PostCalibration Monte Carlo: Settings
The way in which PostCalibration Monte Carlo Analysis in FePEST works is very similar to the previously discussed PreCalibration option. However, postcalibration analysis can benefit from precalibration results (i.e. Jacobian matrix and super parameters from SVDAssist) to generate a set of random realizations resulting in an “almost calibrated” set of parameters. The “almost calibrated” implies that the measurement objective function is reached with minimum effort.
Settings of the PostCalibration Monte Carlo
The operation mode of PostCalibration Monte Carlo is defined in the Optimization Control section of the Problem Settings dialog as shown below.
Activating postcalibration Monte Carlo operation mode in FePEST.
Postcalibration Monte Carlo is similar to the Precalibration Monte Carlo with the exception of the nullspace projection. The Monte Carlo based parameter generation in FePEST, calls the PEST utilities, namely RANDPAR and PNULPAR (one after the other), to create randomly generated parameters that are “almost calibrated”.
The nullspace projection requires the dimension of the solution space (number of super parameters). This information is already known to FePEST as the problem is already calibrated. The user can further select between the Auto or Manual option to set the dimension of the solution space.

Auto: FePEST will run the PEST Utility SUPCALC to determine the number of super parameters in the system and uses this to carry out the nullspace projection.

Manual: the user is prompted for the dimension of the solution space.
Monte Carlo Analysis: PostCalibration settings.
Similar to Precalibration Monte Carlo, the postcalibration mode also allows the user optimize the FEFLOW problem for each sample set. If the Optimize option is active, PEST will do history matching (i.e. run in Estimation mode). This is done relatively quickly as the optimization starts with an “almost calibrated” set of parameters.
Running FePEST under postcalibration Monte Carlo mode
The button Run should be clicked to execute the PostCalibration Monte Carlo mode. Similar to other modes, it first creates the PEST files. In addition to the RANDPAR output files (mc_rand*.par), some new parameter files appear in the working directory under the name mc_nsp*.par. These files contain the “almost calibrated” parameters that result from the PNULPAR utility.
Results of the Postcalibration Monte Carlo Analysis
The Parameter Uncertainty and Observation Uncertainty charts are also available for this mode. The Parameter Uncertainty dialog plots histograms for each parameter definition. Note that the histograms now relate to the parameters after nullspace projection, i.e. “almost calibrated” parameters. Similarly, the Observation Uncertainty dialog plots histograms for each observation definition. Figure below shows an example of these two charts after optimization.
Results of postcalibration Monte Carlo analysis: Observation Uncertainty charts.
If the optimize option was enabled, a table summarizing the parameter values and the measurement objective function can be accessed from the menu Results  Show Results.
Postcalibration Monte Carlo Analysis results.