1. Geog 409: Advanced Spatial Analysis & Modelling © J.M. Piwowar1Principles of Spatial Modelling

2. Geog 409: Advanced Spatial Analysis & Modelling © J.M. Piwowar2Principles of Spatial Modelling Systems Modelling Approach  The process of breaking down highly complex environments into discrete systems so that it can be more easily studied.  Each sub-system will have its own inputs and outputs and interconnected components.  It allows us to focus on that which is of direct interest; everything else is ignored. Hardisty, et al., 1993. Computerised Environmental Modelling. Chichester: Wiley

3. Geog 409: Advanced Spatial Analysis & Modelling © J.M. Piwowar3Principles of Spatial Modelling Environmental Systems  Environmental systems exist over a range of scales: microscopic biota through to the Earth’s climate system  At each scale, the individual components have boundaries (e.g. a leaf’s surface) but are interconnected with other systems at other scales (e.g. sunlight & moisture). D.Draper (2001). Our Environment: A Canadian Perspective, Second Edition

4. Geog 409: Advanced Spatial Analysis & Modelling © J.M. Piwowar4Principles of Spatial Modelling Assumptions 1.It is actually possible to subdivide the real world into discrete, contained, functioning systems. 2.It is possible to determine the various inputs and outputs and interrelationships between system components.

5. Geog 409: Advanced Spatial Analysis & Modelling © J.M. Piwowar5Principles of Spatial Modelling Why Model?  A model represents a simplification of reality.  The intention is to retain the significant features and relationships of reality.  All models are subjective.  The modeller chooses which real-world elements should be included as well as how they are represented.  Models are used to describe, explore, and analyze how a system works; and to test predictive “what if?” scenarios.

6. Geog 409: Advanced Spatial Analysis & Modelling © J.M. Piwowar6Principles of Spatial Modelling Types of GIS Models  There are many different types of model classifications.  Many models can exist in more than one category.  Some models that are separated in one classification may be joined in another classification.

7. Geog 409: Advanced Spatial Analysis & Modelling © J.M. Piwowar7Principles of Spatial Modelling Types of GIS Models  Purpose Models  Descriptive Models  Describe parts or all of a study area.  Passive. e.g. a map.  Prescriptive Models  Prescribe best solutions.  Active. e.g. best location analysis

8. Geog 409: Advanced Spatial Analysis & Modelling © J.M. Piwowar8Principles of Spatial Modelling Types of GIS Models  Logistic Models  Inductive  Builds general models based on individual data.  Moves from specific examples to generalized models.  Useful if we are unaware of the general conditions or rules that govern the modelled features.  Deductive  Straightforward; easily understood.  Logic moves from general to specific.  Useful if we already have substantial preliminary knowledge of what factors are important, how they interact, and which are most important.

9. Geog 409: Advanced Spatial Analysis & Modelling © J.M. Piwowar9Principles of Spatial Modelling Types of GIS Models  Methodological Models  Deterministic  There is only one output for a given input  Unique solutions are obtained  The simplest type of relationship between 2 variables is linear e.g. a = mx + b  Stochastic  There are a range of possible outcomes for any one input; there is no single answer.  Reflects randomness, or uncertainty, in the system  Uncertainty is incorporated through probability e.g. Markov models: the probability of an event occurring is dependent on the event preceding it.  Monte Carlo simulations: take random samples from a stochastic model; the results are independent of previous states of the system

10. Geog 409: Advanced Spatial Analysis & Modelling © J.M. Piwowar10Principles of Spatial Modelling Types of GIS Models  Deterministic  Inductive  Descriptive

11. Geog 409: Advanced Spatial Analysis & Modelling © J.M. Piwowar11Principles of Spatial Modelling Types of GIS Models  Stochastic  Inductive  Prescriptive  Descriptive

12. Geog 409: Advanced Spatial Analysis & Modelling © J.M. Piwowar12Principles of Spatial Modelling Ideal Model Properties  GeneralityRealityPrecision  Only 2 can be adequately represented in any given model.  Analytical or mathematical models focus on generality and precision and predict accurate response within a simplified reality.  Mechanistic or process models are realistic and general and base predictions on functional cause and effect relationships.  Empirical models are precise and realistic and are based on empirical facts. Guisan, A. and Zimmermann, N.E. 2000. Predictive habitat distribution models in ecology. Ecological Modelling 135: 147-186.

13. Geog 409: Advanced Spatial Analysis & Modelling © J.M. Piwowar13Principles of Spatial Modelling The Modelling Process  State Objectives  The first step in model conceptualization is to think about the end results … what do we want the model to produce?  Care must be taken to provide an objective result rather than prescribing the outcome to fit expectations.

14. Geog 409: Advanced Spatial Analysis & Modelling © J.M. Piwowar14Principles of Spatial Modelling The Modelling Process  Define Model Components  Divide the problem into elements and operators.  Recognize spatial patterns.  Identify the processes that created the patterns.  Look for linkages.

15. Geog 409: Advanced Spatial Analysis & Modelling © J.M. Piwowar15Principles of Spatial Modelling The Modelling Process  Find Data  Find data to work with your model; do not make your model work with your data.  Reasons to ignore existing data:  They may not have the necessary scale, accuracy, classification, etc.  They may not have the desired spatial coverage and/or employed appropriate sampling procedures.  They may have too many themes.  Data sets can often bias your thinking.  Many data sets are incomplete.

16. Geog 409: Advanced Spatial Analysis & Modelling © J.M. Piwowar16Principles of Spatial Modelling The Modelling Process  Recognize Spatial Patterns  Sometimes determining the underlying processes that created the patterns; sometimes evaluating the effects of existing patterns on on-going processes.  Go beyond pattern recognition into pattern description. Demers, M.N., 2002. GIS Modeling in Raster. Wiley.