If model parameters are to be estimated using inverse modelling, the following procedure is generally recommended:

 

• The first step should be to start with a relatively coarse zoning of the data, i.e. only a few global parameters are optimised. The evaluation of the inverse modelling runs with a rough zoning usually provides good information as to whether the general zoning makes sense. If this is the case, detailed zoning can be carried out.

• Once the "rough" inverse modelling has been completed, individual parameters can be determined more precisely in sub-areas. It makes sense to remove the areas with sufficiently accurate results from the inverse optimisation. The optimised model data is recorded in the model file and removed from the parameter file. This reduces the number of parameters to be optimised and limits the computational effort for an inverse run.

• There are often areas of the model where only a small amount of observation data is available. It is then usually difficult to find meaningful parameters with the help of inverse modelling. Even if good results have been achieved in the rest of the model area, there are often "outliers" in the optimised parameters in these critical areas. Essentially, there are two ways to get a grip on the parameters in such areas:

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

However, it is also possible to define 'dummy' observation data in these areas: The user can, for example, introduce sensibly estimated additional potential heads as observation points. However, these should then - in contrast to the actual measured potential heads - be given smaller weighting parameters, as they are generally less credible than measured values.

• There are two different approaches to the transition from a coarse zoning to a finer differentiation of parameters:

A zone can be divided into several smaller zones, or the number of parameters within the zone can be increased

 

In general, the results of the optimisation are easier to interpret when using zones with only one parameter (i.e. constant parameters within the zones). If zones with several parameters are used, the results of the optimisation must also be evaluated with regard to the interpolation algorithm used. The optimisation is then also susceptible to weaknesses in the interpolation algorithm used. These are, for example, overshooting or undershooting with Gaussian and Kriging or the tendency for local extremes in the interpolation points when using distance weighting.

 

Evaluation of the sensitivities

Inverse modelling requires the user to constantly check the conceptual model. An evaluation of the sensitivities at the end of each inverse modelling run provides a lot of important information for:

 

• Model areas in which too little information is available can be recognised:

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

• critical and non-critical parameters:

A comparison of the sensitivities shows which of the parameters has the greatest influence on the error at a particular observation point.

• Incorrect modelling assumptions:

If the iteration run diverges or if there is only a minimal error reduction, a general review of the model assumptions (e.g. the division of the zones) is required.

 

Restrictions for the inverse modelling