The field of ecohydraulics integrates hydrodynamic and eco-dynamic processes. While hydrodynamic processes are usually well described by partial differential equations (PDE’s) based on physical conservation principles, ecosystem dynamics often involve specific interactions at the local scale. Because of this, Cellular Automata (CA) are a viable paradigm in ecosystem modelling. All cells in a CA system update their states synchronously at discrete steps according to simple local rules. The classical CA configuration consists of uniformly distributed cells on a structured grid. But in the field of hydrodynamics, the use of unstructured grids has become more and more popular due to its flexibility to handle arbitrary geometries.
The main objective of this research is to identify whether the CA paradigm can be extended to unstructured grids. To that end the concept of Unstructured Cellular Automata (UCA) is developed and various UCA configurations are explored and their performance investigated. The influence of cell size was analyzed in analogy with the Finite Volume Method. A characteristic parameter —min distance of UCA– was put forward and tested by numerical experiments. Special attention was paid to exploring the analogies and differences between the discrete CA paradigm and discrete numerical approximations for solving PDE’s. The practical applicability of UCA in ecohydraulics modelling is explored through a number of case studies and compared with field measurements.
1 INTRODUCTION
1.1 BACKGROUND
1.2 RESEARCH SCOPE
1.3 OBJECTIVES AND RESEARCH QUESTIONS
1.4 THESIS OUTLINE
2 THE CONCEPT OF CELLULAR AUTOMATA
2.1 A BRIEF HISTORICAL OVERVIEW
2.2 CELLULAR AUTOMATA WITH DIFFERENT STRUCTURED LATTICE CONFIGURATIONS
2.3 NEIGHBOURHOOD SCHEMES OF CELLULAR AUTOMATA
2.4 TRANSITION RULES OF CA
2.4.1 Deterministic CA rules
2.4.2 Probabilistic CA rules
2.4.3 Data-driven based rules
2.4.4 Asynchronous rules
2.5 BOUNDARIES OF CA
2.6 BEHAVIOUR AND CLASSIFICATION OF CA
2.7 APPLICATIONS OF CELLULAR AUTOMATA
3 THE CONCEPT OF UNSTRUCTURED CELLULAR AUTOMATA
3.1 MOTIVATIONS TO DEVELOP UNSTRUCTURED CELLULAR AUTOMATA
3.2 CELL CONFIGURATIONS OF UNSTRUCTURED CELLULAR AUTOMATA
3.2.1 Unstructured Cellular Automata with triangle elements
3.2.2 Unstructured Cellular automata with polygon elements
3.3 EFFECTS OF INITIAL CONDITIONS IN UCA
3.3.1 Initial spatial distribution
3.3.2 Initial percentage analysis
3.4 EFFECTS OF DIFFERENT NEIGHBOURHOOD SCHEMES IN UCA
3.4.1 Three-sided type
3.4.2 Moore type UCA
3.4.3 Three-vertex type
3.4.4 Star-like Voronoi polygons
3.5 ANALYSIS AND DISCUSSION
4 COMPUTATIONAL THEORY OF UNSTRUCTURED CELLULAR AUTOMATA
4.1 CELLULAR AUTOMATA RELATIONS WITH OTHER MODELLING METHODOLOGIES
4.1.1 Artificial Life and Cellular Automata
4.1.2 Fractal Theory and Cellular Automata
4.1.3 Markov Processes and Cellular Automata
4.1.4 Diffusion-Limited Aggregation model (DLA) and Cellular Automata
4.1.5 Individual Based Model (IBM) and Cellular Automata
4.2 CELLULAR AUTOMATA AND PARTIAL DIFFERENTIAL EQUATIONS
4.2.1 Analogies and differences between CA and PDEs
4.2.2 General comparison of CA and PDE
4.3 EFFECTS OF CELL SIZE IN UNSTRUCTURED CELLULAR AUTOMATA
4.3.1 Original meshes & Locally refined meshes
4.3.2 Rough meshes & Globally refined meshes
4.3.3 Analysis and discussion
5 UNSTRUCTURED CELLULAR AUTOMATA FOR SPATIAL DYNAMIC ECOLOGICAL MODELLING
5.1 UCA FOR PREY-PREDATOR MODEL
5.2 UCA FOR ALGAE BLOOM MODEL
5.3 SPATIAL WATER QUALITY MODEL FOR SPIKED POLLUTION
5.3.1 Non-uniform diffusion water quality model
5.3.2 Application for study case (Numerical experiment)
6 SPATIAL EVOLUTION OF BENTHONIC MACROINVERTEBRATE UNDER FLOW REGULATION USING HYBRID MODELLING
6.1 INTRODUCTION
6.1.1 Description of study area
6.1.2 Data Collection
6.2 HYBRID MODEL DEVELOPMENTS
6.2.1 Two-dimensional water quality module
6.2.2 macroinvertebrate habitat module
6.2.3 Model verification
6.2.4 Scenario analyses
6.3 QUANTIFY SPATIAL DISTRIBUTION OF MACROINVERTEBRATE USING CELLULAR AUTOMATA
6.3.1 Patch analysis of macroinvertebrate habitat using cellular automata
6.3.2 Cellular automata Homogeneity
6.4 RESULTS AND DISCUSSIONS
7 INDIVIDUAL-BASED AND SPATIAL-BASED UNSTRUCTURED CELLULAR AUTOMATA AND APPLICATION TO AQUATIC ECOSYSTEM MODELLING
7.1 DESCRIPTION OF STUDY AREA
7.2 INFLUENCING FACTORS FOR WATER LILY GROWTH
7.3 SPATIAL-BASED UCA MODEL SETUP
7.4 INDIVIDUAL BASED MODELLING USING UNSTRUCTURED CELLULAR AUTOMATA
7.5 ANALYSIS OF RESULTS
7.6 FUTURE STUDY
8 CONCLUSIONS AND RECOMMENDATIONS
CONCLUSIONS
RECOMMENDATIONS FOR FUTURE WORK
REFERENCES
APPENDICES
ABOUT THE AUTHOR
Biography
Ms. Yuqing LIN is from China and obtained her Master of Science degree in Hydroinformatics (with distinction) in 2008 at UNESCO-IHE in Delft, the Netherlands. She continued as a fulltime PhD fellow at Deltares, Delft University of Technology and UNESCO-IHE, conducting her research on ‘Unstructured Cellular Automata in Ecohydraulics Modelling’. Her research interests include: mathematical modelling, ecohydraulics, unstructured cellular automata and environmental hydroinformatics.
