Paradigm Shifts in Parameter Space

There exists a long going discussion on how many parameters are needed within complex ecological, ecosystem and earth system models. Overparameterization is an often-used term to describe an overshoot in parameter space dimensionality, which sometimes may lead to better results, but goes hand in hand with a loss in generality. Oversimplification of parameter space dimensions - on the other hand - may lead to results that may be correct in the mean, but incorrect in each single case.

So, one question arises: How can we determine the number of parameters needed to describe a system with the desired accuracy and precision for a given application?

A possible answer lies in the relationship between the correlation among, and the respective information content within, some given data or model outputs. Alfréd Rényi provided dimensional descriptors for this issue, i.e. the correlation dimension and the information dimension embedded in a given data series.

When both dimensions are equal, the most simple model description with least parameters is best. When information content exceeds the correlation, then a higher dimensional parameter space is needed to achieve accurate results.

We will use two examples to demonstrate this principle: temperate alpine ecosystems and tropical lowland ecosystems, both modelled with BGC-MAN. The degree of difference between correlation and information will show the differences in parameter space needed to get an accurate and precise description of the modelled system.