Unstructured cellular automata for modelling macrophyte dynamics

Due to the complexity of ecohydraulic systems, it is hard to derive general physical equations that describe all processes in sufficient detail. Quite often non-linear local interactions play a dominant role, in particular for ecosystems in the aquatic environment. In recent years, the cellular automata (CA) paradigm was successfully applied to ecohydraulic systems and proved to be a useful approach in, e.g. population dynamics modelling. CA constitute a mathematical system in which many simple components act together to produce complicated patterns of behaviour. Most of the previous applications of CA in ecohydraulic modelling are conventionally based on regularly spaced, structured meshes. However, hydraulic flow and transport modelling nowadays are often making use of unstructured computational meshes that provide more flexibility for fitting complicated geometries and that can be locally refined if needed to deal with, e.g. patchiness of the vegetation. In this paper, the concept of CA is extended to unstructured meshes, using a model for water lily growth and decay in a small pond during half a year as a sample case study. Two types of unstructured cellular automata (UCA) were developed to capture growth patterns of water lily plants. One is referred to as spatial-based UCA modelling, the other as individual-based UCA modelling. The modelling results are compared with high-resolution photographs obtained on a weekly basis. In addition, a three-dimensional UCA model is outlined in which the evolution of water lilies in the vertical direction can be taken into account as well.