General procedure

If model parameters are estimated by inverse modelling, the following procedures are generally recommended:

The inverse modelling should at first be started with a relatively coarse zoning of the data, i.e., only a few global parameters are optimized. The evaluation of the inverse modelling with a coarse zoning usually provides good information about whether the general zoning is appropriate. If this is the case, detailed classifications can be made.

If the “coarse” inverse modelling is completed individual parameters can be further refined in some areas. It makes sense to take out the areas with sufficiently accurate results from the inverse optimization. The optimized model data are required in the model file and removed from the parameter file. This reduces the number of parameters to be optimized and limits the computational cost for an inverse calculation.

Often there are areas of the model in which there are only a few observation data. Then it is usually difficult to find meaningful parameters using the inverse modelling. Even if good results in the rest of the model area are achieved, there are often "runaways" in the optimized parameters of these critical areas. There are essentially two options, to get a grip on the parameters in areas with such little information:

The parameters are removed from the inverse modelling and specified with an estimated plausible value in the model file.

There is also the possibility to assign “dummy” observation data in this area: the user can, for example, introduce estimated additional potential heads as observation data. These should then get smaller weighting parameters - as opposed to the actual measured potentials - because they are less credible than typically measured values.

For the transition from a coarse to a finer differentiation of the zoning parameters, there are two different approaches:

A zone can be divided into smaller zones, or

The number of parameters within the zone can be increased.

In general, the results of the optimization are to be interpreted more easily when using zones with only one parameter ( constant parameters within the zones). If zones with multiple parameters are used, the results of the optimization have to be evaluated according to the used interpolation algorithm. The optimization is then additionally vulnerable to weaknesses in the used interpolation algorithm. These are for example over- or under oscillations in Gauss and Kriging, or the tendency to local extrema in the interpolation using the distance weighting.

Evaluation of the sensitivities

The inverse modelling requests constantly a review by the user of the conceptual model. An evaluation of the sensitivities at the end of each inverse calculation provides this important information:

Model areas where are not enough information can be detected:

If all parameters in a model area show only small sensitivities, this area should either provided with additional observational data or be removed from the calibration.

Critical and non-critical parameters:

When comparing the sensitivities it is obtained, which of the parameters has the greatest influence on the error in a defined observation point.

Wrong model assumptions:

If the iteration diverges or there is only a minimal reduction of errors a general review of the model assumptions (e.g. the distribution of the zones) is required.

Restrictions for the inverse modelling