Toward a Method to Generally Describe Physical Spatial Processes

  • Barbara Hofer
  • Andrew U. Frank
Conference paper
Part of the Lecture Notes in Geoinformation and Cartography book series (LNGC)


Spatial processes are the focus of geography and should play a prominent role in geographic information systems (GIS). However, current GIS focus on the static description of properties in space and do not systematically support processes. A general method to describe spatial processes is a prerequisite to including processes in GIS software. This paper outlines an attempt to a general and application independent method to describe processes, limited currently to physical spatial processes. The methodology is based on first modeling a process with a deterministic model. The deterministic models employed here divide the region of interest into blocks and define the influence of the process on each block. The resulting model equations are then related to partial differential equations (PDEs), which are an alternative method for describing processes. Thereby, the qualitative characteristics of processes are identified. A method for describing processes has to be capable of covering the identified characteristics of the processes. As an example the process of diffusion of a contaminant in water is analyzed. The results of this study suggest that this approach allows identifying commonalities among spatial physical processes. These insights can lead to a set of types of processes on which a method to describe spatial processes can be based in the long run.


spatial physical processes deterministic models partial differential equations 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abel DJ, Taylor K, Kuo D (1997) Integrating modelling systems for environmental management information systems. SIGMOD Record. 26: 5-10CrossRefGoogle Scholar
  2. Abler R, Adams JS, Gould P (1977) Spatial Organization: the Geographer’s View of the World. Prentice-Hall International, LondonGoogle Scholar
  3. Albrecht J (1998) Universal Analytical GIS Operations - A task-oriented systematisation of data-structure-independent GIS functionality. In: Craglia M, Onsrud H (eds.) Geographic Information Research - Trans-Atlantic Perspectives. Taylor & Francis, London. 577-591Google Scholar
  4. Batty M (2005) Network Geography: Relations, Interactions, Scaling and Spatial Processes in GIS. In: Unwin D, Fisher P (eds.) Re-Presenting GIS. Wiley, Chichester, UK.Google Scholar
  5. Batty M, Xie Y, Sun Z (1999) Modeling urban dynamics through GIS-based cellular automata. Computers, Environment and Urban Systems 23(3): 205-233CrossRefGoogle Scholar
  6. Bivand RS, Lucas AE (2000) Integrating Models and Geographical Information Systems. In: Openshaw S, Abrahart RJ (eds.) GeoComputation. Taylor & Francis, London. 331-363Google Scholar
  7. Blok C (2000) Monitoring Change: Characteristics of Dynamic Geo-spatial Phenomena for Visual Exploration. In: Freksa C, Brauer W, Habel C, Wender KF (eds.) Spatial Cognition II, Integrating Abstract Theories, Empirical Studies, Formal Methods, and Practical Applications. Springer-Verlag, Berlin Heidelberg. 1849: 16-30Google Scholar
  8. Cliff AD, Ord JK (1981) Spatial Processes - Models & Applications. Pion, LondonGoogle Scholar
  9. Frank AU (1998) GIS for politics. CD-ROM Proceedings of the GIS Planet 1998 Conference, Lisbon, PortugalGoogle Scholar
  10. Frank AU (2001) Tiers of ontology and consistency constraints in geographic information systems. International Journal of Geographical Information Science (IJGIS) 75(5): 667-678CrossRefGoogle Scholar
  11. Frank AU (2007) Material vs. information causation-An ontological clarification for the information society. Wittgenstein Symposium in August 2007, Kirchberg, Austria: 5-11Google Scholar
  12. Getis A, Boots B (1978) Models of Spatial Processes - An approach to the study of point, line and area patterns. Cambridge University Press, CambridgeGoogle Scholar
  13. Giudici M (2002) Development, Calibration, and Validation of Physical Models. In: Clarke K, Parks B, Crane M (eds.) Geographic Information Systems and Environmental Modeling. Prentice Hall, Upper Saddle River, N.J.: 100-121Google Scholar
  14. Goodchild MF, Yuan M, Cova TJ (2007) Towards a general theory of geographic representation in GIS. International Journal of Geographical Information Science (IJGIS) 21(3): 239-260CrossRefGoogle Scholar
  15. Hohage T (2004) Skriptum - Partielle Differentialgleichungen. Göttingen, Universität.Google Scholar
  16. Hornsby K (1996) Spatial diffusion: conceptualizations and formalizations. NCGIS Specialist Meeting on Formal Models of Commonsense Geographic Worlds, San Marcos, TexasGoogle Scholar
  17. Hornsby K, Egenhofer MJ (1997) Qualitative Representation of Change. In: Hirtle SC, Frank AU (eds.) Spatial Information Theory - A Theoretical Basis for GIS (International Conference COSIT’97). Springer-Verlag, Berlin-Heidelberg. 1329: 15-33Google Scholar
  18. Kemp KK (1992) Environmental Modeling with GIS: A Strategy for Dealing with Spatial Continuity. Ph.D. thesis, University of California, Santa Barbara.Google Scholar
  19. Logan JD (2004) Applied Partial Differential Equations. Springer-Verlag, New YorkGoogle Scholar
  20. MacEachren AM (1995) How Maps Work - Representation, Visualization and Design. Guilford Press, New YorkGoogle Scholar
  21. Markowich PA (2007) Applied Partial Differential Equations: A Visual Approach. Springer Verlag, Berlin HeidelbergGoogle Scholar
  22. Miller HJ, Wentz EA (2003) Representation and spatial analysis in geographic information systems. Annals of the Association of American Geographers 93(3): 574-594CrossRefGoogle Scholar
  23. Mitasova H, Mitas L (2002) Modeling Physical Systems. In: Clarke K, Parks B, Crane M (eds.) Geographic Information Systems and Environmental Modeling. Prentice Hall, Upper Saddle River, N.J.: 189-210Google Scholar
  24. Reitsma F, Albrecht J (2005) Implementing a new data model for simulation processes. International Journal of Geographical Information Science (IJGIS) 19(10): 1073-1090CrossRefGoogle Scholar
  25. Seppelt R (2005) Simulating invasions in fragmented habitats: theoretical considerations, a simple example and some general implications. Ecological Complexity 2(3): 219-231CrossRefGoogle Scholar
  26. Thomas RW, Huggett RJ (1980) Modelling in Geography - A Mathematical Approach. Harper & Row, LondonGoogle Scholar
  27. Tobler W (1970) A computer movie simulating urban growth in the Detroit region. Economic Geography 46(2): 234-240CrossRefGoogle Scholar
  28. Tobler WR (1981) A Model of geographical movement. Geographical Analysis 13(1): 1-20Google Scholar
  29. Tomlin CD (1990) Geographic Information Systems and Cartographic Modeling. Prentice Hall, New YorkGoogle Scholar
  30. Van Deursen WPA (1995) Geographical Information Systens and Dynamic Models. Ph.D. thesis, NGS Publication, Faculty of Spatial Sciences. University of Utrecht, Utrecht.Google Scholar
  31. Worboys MF (2005) Event-oriented approaches to geographic phenomena. International Journal of Geographical Information Science (IJGIS) 19(1): 1-28CrossRefGoogle Scholar
  32. Yuan M (2001) Representing complex geographic phenomena in GIS. Cartography and Geographic Information Science 28(2): 83-96CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Barbara Hofer
    • 1
  • Andrew U. Frank
    • 1
  1. 1.Department of Geoinformation and CartographyVienna University of TechnologyGusshausstrasse 27-29 E127Austria

Personalised recommendations