The use of canonical S-system modelling for condensation of complex dynamic models

A method is introduced for purposefully simplifying complex process-based models in cases where only part of the system dynamics is to be investigated. To be generally applicable, the approach of model condensation is based upon canonical non-linear modelling using S-system type models. These models consist of a set of differential equations of standardized type. As they are versatile and dynamic systems these models are adequate tools for the simplification of process-based models. The S-system equations are built up deterministically by reflecting interactions and processes of the complex model (or the real system). For the estimation of the particular parameter values, there should be observed data for rates of change or for the development of the state variables. Considering the lack of such information in practice, alternative `pseudo observed dataʹ are generated using the complex model after estimating its uncertain parameter values with an evolutionary algorithm. To illustrate the procedure, an example is given for a `site yield tableʹ-like model condensed from a process-oriented model for even-aged pure forest stands, TREEDYN3. Dynamics of tree height, diameter at breast height, number of trees, and canopy closure of a spruce (Picea abies [L.] Karst.) stand are simulated with thinning intensity as controlling variable. Though numbers of variables and parameters are reduced drastically and equations are of simple form, under a variety of different thinning scenarios the condensed model proves to be a good representation of the complex one for the system segment under consideration.