This document discusses different types of models used for modeling spatial processes in GIS for decision support. It describes natural and scale analogue models which use real-world events or objects as analogues. Conceptual models represent processes visually using diagrams. Mathematical models include deterministic, stochastic, and optimization models. Deterministic models show direct relationships while stochastic models use probabilities. Optimization models maximize or minimize outputs. The document argues that combining different modeling techniques in GIS allows for complex spatial process modeling to support decisions.

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