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UNIT 9 -- CALIBRATION:

Recall that calibration is the process of adjusting parameter values, boundary conditions, model conceptualization, and/or model construction until the model simulation matches field observations. This activity is necessary because the field measurements are not accurate reflections of the model scale properties. Field measurements sample a variety of scales and time periods. Calibration of a model allows for adjustment of the parameters to accommodate an integrated interpretation of the system.

The final values resulting from the calibration should correspond with field measurements. When the values differ significantly from the values that are expected, one needs to carefully consider whether such a difference is reasonable due to scale issues, whether the conceptual model is in error, or whether there are errors in the field data. This process is much like the process we discussed when applying analytical models. That is, have expectations and question all aspects of the situation when you calculations do not match your expectations.

I have an entire course on automated calibration (which is also referred to as inversion or parameter estimation). It is a valuable tool, not only for finding the best fit to your field observations, but also for identifying the type and location of additional data that will be most helpful, and for differentiating conceptual models and identifying those models that are most representative of the field.

Unfortunately, for the most part, practicing ground-water professionals are still using trial-and-error calibration. I believe this is due to a combination of not understanding the requirements and benefits of inversion and partly because they do not want to take the time to learn more about it. There is no doubt that the time taken to learn to do this will be gained back through its use in a very short time.

We will start with a little trial-and-error calibration, so you get a feel for it. Then I will give you some guidance and public domain inversion codes, MF2K and UCODE, and tell you enough about automated calibration to be "dangerous." Then you can use automated calibration to complete the calibration project. We will discuss automated calibration more as the semester continues. Then you can go on to learn the rest on your own, or take an inversion class.

CALIBRATION EXERCISE

Trial and error calibration (also known as parameter estimation, optimzation, inversion, regression) is tedious and does not provide the insight that can be obtained using automated calibration, so we will use nonlinear regression to accomplish this task via UCODE_2005.

First set up your MODFLOW simulation to print the simulated equivalents to the observations (these will be in the _os file)
Setting up observations with MF2K
Sensitivities are needed for parameter estimation. These can be calculated by MODFLOW using exact derivatives for some parameters and observation types. This is faster and more accurate than using perturbation methods. However often we want to estimate parameters or a combination of parameters that MODFLOW is not coded for. For example, MODFLOW cannot make a conductance for a drain as a function of an aquifer hydraulic conductivity. Items for which MODFLOW cannot calculate sensitivities, can be evaluated for sensitivity by perturbation using UCODE. Whether or not MODFLOW is used to calculate the sensitivities, it is useful to set up an input file for the sensitivity process because this is the most convenient way to enter the adjusted parameters during calibration. So next we will set up sensitivity evaluation using the MODFLOW sensitivity package.
Setting up sensitivity calculations with MF2K
Currently there is a parameter estimation package in MODFLOW (PES) which is limited to estimating parameters using observations for which exact derivatives have been coded into MF2K. Eventually this package will be discontinued and parameter estimation will only be accomplished using UCODE, so we will work with that. The sensitivites can be caculated using MODFLOW or UCODE or a combination of the two. At first, for simplicity, and because your model runs quickly, we will use UCODE both to calculate sensitivity by perturbation and to optimize the parameters,
Parameter estimation with UCODE

COMMUNICATION

Please bring up any concerns you may have about calibration. epoeter@mines.edu

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