Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Abel DJ, Taylor K, Kuo D (1997) Integrating modelling systems for environmental management information systems. SIGMOD Record. 26: 5-10
Abler R, Adams JS, Gould P (1977) Spatial Organization: the Geographer’s View of the World. Prentice-Hall International, London
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. 577-591
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.
Batty M, Xie Y, Sun Z (1999) Modeling urban dynamics through GIS-based cellular automata. Computers, Environment and Urban Systems 23(3): 205-233
Bivand RS, Lucas AE (2000) Integrating Models and Geographical Information Systems. In: Openshaw S, Abrahart RJ (eds.) GeoComputation. Taylor & Francis, London. 331-363
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: 16-30
Cliff AD, Ord JK (1981) Spatial Processes - Models & Applications. Pion, London
Frank AU (1998) GIS for politics. CD-ROM Proceedings of the GIS Planet 1998 Conference, Lisbon, Portugal
Frank AU (2001) Tiers of ontology and consistency constraints in geographic information systems. International Journal of Geographical Information Science (IJGIS) 75(5): 667-678
Frank AU (2007) Material vs. information causation-An ontological clarification for the information society. Wittgenstein Symposium in August 2007, Kirchberg, Austria: 5-11
Getis A, Boots B (1978) Models of Spatial Processes - An approach to the study of point, line and area patterns. Cambridge University Press, Cambridge
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.: 100-121
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): 239-260
Hohage T (2004) Skriptum - Partielle Differentialgleichungen. Göttingen, Universität.
Hornsby K (1996) Spatial diffusion: conceptualizations and formalizations. NCGIS Specialist Meeting on Formal Models of Commonsense Geographic Worlds, San Marcos, Texas
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: 15-33
Kemp KK (1992) Environmental Modeling with GIS: A Strategy for Dealing with Spatial Continuity. Ph.D. thesis, University of California, Santa Barbara.
Logan JD (2004) Applied Partial Differential Equations. Springer-Verlag, New York
MacEachren AM (1995) How Maps Work - Representation, Visualization and Design. Guilford Press, New York
Markowich PA (2007) Applied Partial Differential Equations: A Visual Approach. Springer Verlag, Berlin Heidelberg
Miller HJ, Wentz EA (2003) Representation and spatial analysis in geographic information systems. Annals of the Association of American Geographers 93(3): 574-594
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.: 189-210
Reitsma F, Albrecht J (2005) Implementing a new data model for simulation processes. International Journal of Geographical Information Science (IJGIS) 19(10): 1073-1090
Seppelt R (2005) Simulating invasions in fragmented habitats: theoretical considerations, a simple example and some general implications. Ecological Complexity 2(3): 219-231
Thomas RW, Huggett RJ (1980) Modelling in Geography - A Mathematical Approach. Harper & Row, London
Tobler W (1970) A computer movie simulating urban growth in the Detroit region. Economic Geography 46(2): 234-240
Tobler WR (1981) A Model of geographical movement. Geographical Analysis 13(1): 1-20
Tomlin CD (1990) Geographic Information Systems and Cartographic Modeling. Prentice Hall, New York
Van Deursen WPA (1995) Geographical Information Systens and Dynamic Models. Ph.D. thesis, NGS Publication, Faculty of Spatial Sciences. University of Utrecht, Utrecht.
Worboys MF (2005) Event-oriented approaches to geographic phenomena. International Journal of Geographical Information Science (IJGIS) 19(1): 1-28
Yuan M (2001) Representing complex geographic phenomena in GIS. Cartography and Geographic Information Science 28(2): 83-96
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hofer, B., Frank, A.U. (2008). Toward a Method to Generally Describe Physical Spatial Processes. In: Ruas, A., Gold, C. (eds) Headway in Spatial Data Handling. Lecture Notes in Geoinformation and Cartography. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68566-1_13
Download citation
DOI: https://doi.org/10.1007/978-3-540-68566-1_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-68565-4
Online ISBN: 978-3-540-68566-1
eBook Packages: Earth and Environmental ScienceEarth and Environmental Science (R0)