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MODELS OF SPATIAL PROCESSES

NATURAL & SCALE ANALOGUE MODELS

CONCEPTUAL MODELS

MATHEMATICAL MODEL

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- 1. GIS-MODELLING FOR DECISION SUPPORT: MODELS OF SPATIAL PROCESSES: NATURAL & SCALE ANALOGUE MODELS CONCEPTUAL MODELS MATHEMATICAL MODEL Represented By Sushant Sawant Mtech I Geoinformatics
- 2. Introduction • Models of spatial form are represented and analyzed using GIS. These models can be used in many ways in data analysis operations; however , they tell us nothing about the process responsible for creating or changing spatial form. • E.g. Population change, climate change, soil erosion. Etc.
- 3. Models of spatial process • A process model simulates “real – world processes”. • There are “2 reasons” for constructing such a model. • 1. From a “pragmatic point of view” decision- need to be made and actions taken about spatial phenomena. Model help this process. • 2. From a “philosophical point of view” a process model may be the only way of evaluating our understanding of the complex behavior of spatial systems.( Buck et.al., 1995).
- 4. Why a classification of process models is a good first step? • There are many different approaches to process modelling • To decide which is appropriate in a particular situation • An understanding of the range of models available, their strengths and weakness
- 5. Classification of process models • 1. a priori • 2. a posteriori
- 6. Priori models A “priori models” are used to model processes for which a body of theory has yet to be established. In these situations the models is used to help in the search for theory. E.g. Scientist involved in research to establish whether – global warming is taking place, would use a priori models, as the phenomenon of “global warming” is still under investigation.
- 7. Posteriori Models • “Posteriori Models” on the other hand, are designed to explore an established theory. These models are usually constructed when attempting to apply theory to new areas. • An a posteriori model might be developed to help predict avalanches in a mountain area where a new ski piste has been proposed. E.g. Avalanche formation theory is responsible, well established, and several models already exist which could be applied to explore the problem.
- 8. • Beyond the a priori / a posteriori division, developing a further classification of process models becomes quite complex. • However, 2 useful classifications ( Hardisty et al., 1993; Steyaert, 1993) have been integrated here to provide a starting point for examining the different types of models. • The classification includes: 1. natural and scale analogue models. 2. conceptual models. 3. mathematical models.
- 9. NATURAL & SCALE ANALOGUE MODELS • Natural analogue models: uses actual “events or real-world” objects as a basis for model construction (Hardisty et al., 1993). • These events or objects occur either in “different places or at different times”. • E.g. a natural analogue model to predict area the formation of avalanches in the previously unstudied area of a new ski piste might be constructed by observing how avalanches form in an area of similar character. • The impact that avalanches would have on the proposed ski piste could also be examined by looking at experiences of ski piste construction in other areas.
- 10. SCALE ANALOGUE MODELS • There are also scale analogue models (Steyaert,1993) such as topographic maps & aerial photographs, which are scaled down and generalized replicas of reality. • These are exactly the sort of analogue models that GIS might use to model the analogue prediction problem.
- 11. CONCEPTUAL MODELS • Conceptual process models are usually expressed in verbal or graphical form, and attempt to describe in words or pictures qualitative & quantitative interactions between real-world features. • The most common conceptual model is a systems diagram, which uses symbols to describe the main components & linkages of the model.
- 12. SIMPLIFIED CONCEPTUAL MODEL OF AVALANCHE PREDICTION
- 13. MATHEMATICAL MODELS • Mathematical process models use a range of techniques including: 1. deterministic 2. stochastic & 3. optimization models.
- 14. Deterministic • There is only one possible answer for a given set of inputs. For example, a deterministic avalanche prediction model might show a linear relationship between slope angle & size of avalanche. • E.g. The steeper the slope, the smaller the avalanche which results, since snow build-up on the slope will be less. • Such models work well for clearly defined, structured problems in which a limited number of variables interact to cause a predictable outcome. • However few simple linear relationships exist in geographical phenomena. • In most situations there is a degree of randomness, or uncertainty, associated with the outcome. • E.g. this is true in the avalanche example.
- 15. Stochastic model • Where there is uncertainty about the nature of the process involved, a mathematical model known as a stochastic model is needed. • Stochastic models recognize that there could be a range of possible outcomes for a given set of inputs, and express the likelihood of each one happening as a probability. • We know that slope angle and size of avalanche are related but that the problem is much more complex than suggested by our deterministic models. • However, in reality other variables will be involved, for example direction of slope, exposure to wind, changes in temperature and underlying topography. • • The predicted size of an avalanche is based on the probability of a number of
- 16. Optimization model • These models are constructed to maximize or minimize some aspect of the models output. • To help identify the area of minimum avalanche risk at a given time..
- 17. Process Modelling & GIS • • • • • • In GIS all the approaches – natural and scale analogue, conceptual & mathematical modeling – are used to model spatial processes. They may be used in isolation, substituted for each other in an interactive development process or combined in an larger, more complex model. The given case study shows how different modeling techniques can be used together to build up complex models of spatial processes. Unfortunately, proprietary GIS software provides few process models as part of the standard set of functions. Thus, generic models, which could be made available in GIS, would be far too inflexible for widespread use. In addition, many of the analytical functions provided by other modelling software, provide an environment for constructing application-specific models.
- 18. References • Heywood, I., Comelius, S., and Carver, S., (1988). An Introduction to Geographical Information Systems, Addison Wiley Longmont, New York. • Burrough, P. A., and McDonnell, R., (2000). Principles of Geographical Information Systems, Oxford University Press, London. • Research paper on Decision Support Systems by Marek J. Druzdzel and Roger R. Flynn, Decision Systems Laboratory, School of Information Sciences and Intelligent Systems Program, University of Pittsburgh, Pittsburgh, PA 15260

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