Environmental Modeling and Models

1. Purposes of models
        Simulate the real World
        Simplify the complex reality
        Explain underlying principles and relationships
        Predict the unknown in space or time
        Test hypothesis and scenarios
 
 2. Component of a model     
        Elements - variables
        Function - relationships between variables, complex/simple
        Explanation - logic behind functions
        Prediction - at other locations or time
                           under different conditions

3. Type of models
        Research models - a research tool
        Management models - a management tool

        Conceptual models - no numerical values or formula
        Theoretical models - with numerical values or formula

        Physical models - based on physical laws, first principle
        Empirical models - based on observations, but the mechanism is unknown

        Deterministic models - based on known physical laws
        Stochastic models - bases on the concept of randomness and probability

        Differential models - based on differential equations
        Matrix models - based on matrix algebra

        Reductionistic models - include as many details as possible
        Holistic models - use general principles

        Static models - behavior of variables not depend on space and time
        Dynamic models - behavior of variables is a function of space and time

        Distributed models - value of parameters depend on space and time
        Lumped models - parameter values are constant

        Linear models - first degree equations
        Non-linear models - one or more equations not first degree

        Causal models - input, state, and output are related to physics laws
        Black-box models - input and output are statistically related   

        Binary/nominal
                    yes/no, present/absent, on/off, true/false, 1/0
        Ranking/ordinal
                    high, medium, low
        Quantitative/interval/ratio
                    absolute numbers, actual amount

4. Performance of a model
        Calibration
                calibrate model parameters based on data that are used to develop the model
        Validation
                validate a model using independent data
        Sensitivity analysis
                sensitivity of model output to changes in model input
        Error propagation
                errors and uncertainty of input data transmitted to the results through
                the modeling process

5. Linking GIS and models
        Direct use of GIS functions
                    suitability index models and the Delphi approach
        Integrating GIS with statistical analysis
                    use statistics to test a GIS model or
                    use GIS to spatialize a statistical model      
        Interfacing GIS with process models
                    GIS provides input data for models and
                    displays the model output
                   
        Integration between GIS and process models
                    develop models in GIS
                    develop GIS in a model
                    interface GIS with models

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