III. CONCEPTS OF MODELLING II.

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1 III. CONCEPTS OF MODELLING II. 5. THE MODELLING PROCEDURE 6. TYPES OF THE MODELS 7. SELECTION OF MODEL TYPE 8. SELECTION OF MODEL COMPLEXITY AND STRUCTURE 1 5. MODELLING PROCEDURE Three significant steps in the modelling procedure: - Verification - Calibration - Validation - All steps of the procedure are used very carefully. - Presented modelling procedure presented is accepted in modelling community. 2 1

2 5. The modelling procedure: Verification - The step that follows the selection of mathematical equations. - Answer to the following question is needed: Is the model stable in long term? State variables should are maintained at approximately the same levels despite variations of forcing functions ==> first running period the model is sensitive to initial conditions stability of the model must be achieved also under long term vales The modelling procedure: Verification Does the model react as expected? To compare model results with observations and changes of the model are made according to the modeler s intuition and knowledge of the reactions of the model. Its time to play with a model and evaluate the model outputs. ==> we use the knowledge about the system which we simulate ==> model should be useful description of real ecosystem 4 2

3 5. The modelling procedure: Verification Are applied units in the model consistent? -Equations should use consistent unites 5 5. The modelling procedure: Sensitivity analysis Get an overview of the most sensitive components of the model. To provide a measure of sensitivity of either parameters, forcing functions or submodels to the state variables of greatest interest in the model. The relative change in parameter value is chosen based on knowledge of the certainty of the parameters. It enables to distinguish between high (high impact on the system behavior) and low (low impact) leverage variables. Low leverage variables may be excluded from the model => effect on complexity and structure of the model => lower complexity => simpler dataset => higher certainty of the model. 6 3

4 5. The modelling procedure: Calibration The scope is to improve the parameter estimation (exact value or range of values of the interval): the parameter set that gives the best agreement between model output and measured values is chosen. Selection of parameter s values: - from literature - from experiments - one value or set of values from an interval 7 5. The modelling procedure: Calibration -To select the most important parameters and experiment with the variation of their values (software for automatic calibration) => time consumable or not applicable at all: (10 parameters, 15 possible values of each parameter = experiments = this is higher number then is the number of seconds since the big bang - The quality of calibration depends the most on the quality of data. 8 4

5 5. The modelling procedure: Calibration Recommendations for the calibration procedure: - Find as much as possible parameters from the literature, otherwise determine them by experiments in situ -Use sensitivity analysis to find the most important parameters. - Use an intensive data collection program for the most important state variables to provide better estimation for the most important parameters - Perform calibration using data not yet applied in order to get acquainted with the model s reactions to changes in parameters. - Repeat sensitivity analysis and try to make fine tuning of parameter s values 9 5. The modelling procedure: Validation - To test the model against an independent set of data to see how well the model simulations fit these data. - The validation is always required (to get a picture about the reliability od the model) - Data for validation must not be the same as was used for calibration. - Data need to be from wide range of forcing functions - Validation criteria (i.e. how good is the model) must be formulated on objectives of the model and the quality of the available data. 10 5

6 11 6. TYPES OF MODELS 12 6

7 6. TYPES OF MODELS Two types of models (according to the application): - Scientific models - tools for testing hypothesis - Management models tools for management TYPES OF MODELS Stohastic models: - contains: => stohastic input disturbance => random measurement errors - If both assumed to be 0 : stohastic model => deterministic model - rarely applied in ecology The predicted values depend on probability distribution. (2) Stohasic disturbance (3) Random measurement errors (1)Measured inputs System state (4) Measured outputs 14 7

8 6. TYPES OF MODELS Deterministic models: - responses of the model are completely determined with: - knowledge of the present state - future measured inputs The predicted values are computed exactly TYPES OF MODELS Reductionistic models: - To incorporate as many details as possible in the model => to capture the behavior of the system - The properties of the system are the sum of details Include as many details as possible 16 8

9 6. TYPES OF MODELS Holistic models: -To include into the model system properties of the ecosystem by using general principles. - Properties of the system are not the sum of all details => system poses additional properties because the subsystems are working as unite Use of general principles TYPES OF MODELS Dynamic models: - System s responses to external factors are described: - by differences equations : use discrete time steps for description of the state of the system - by differential equations: use continues changes of the state variables - Description of the steady state: difference equations - Description of oscillations around steady state: differential e. The variables defining the system are a function of time. 18 9

10 6. TYPES OF MODELS Static models: - all variables and parameters are independent of time - they simplify computation - they may give unrealistic results because they don t respect oscillations which cause that state variables may obtain higher average values The variables defining the system are not dependent on time TYPES OF MODELS Black-box models: - what changes in the inputs will affect the ouput respons -Internal structure of the mode is not known - Relationship between inputs and outputs is find by statistics (or other methods (e.g. data mining) - Limited application in cases where the knowledge about the system is limited The input disturbances affect only the output response No causality required

11 7. SELECTION OF THE MODEL TYPE Depends on: - the problem - the ecosystem characteristics - available data SELECTION OF MODEL TYPE Four focal recommendations on the selection of the model: 1) Model is only as reliable as its least reliable input, balanced complexity on the submodels are recommended. 2) Keep the model as simple as possible and as complex as needed

12 7. SELECTION OF MODEL TYPE 3) Model should have right structure the most important output from the model is better understanding of the system. 4) Maintain system thinking. The model is not a correct representation of the reality but an attempt to describe important system features of the system-problem complex SELECTION OF MODEL COMPLEXITY AND STRUCTURE The selection of the model complexity is the matter of balance: Must include state variables and the processes essential for the problem in focus. Data request: not to make model more complex the the data set can bear. Complexity of model =f (knowledge of processes and state variables, datasets) Its easy to add more equations and state variables to the model => much harder to get needed data for calibration and validation of the model

13 8. SELECTION OF MODEL COMPLEXITY AND STRUCTURE The base model (Zeigler) => the model that will be capable of accounting for the complete input output behavior of real ecosystem and be valid for all frames => ideal model => ecosystem is very complex => the base models should be very complex as well => it is impossible to make a base model of ecosystem. Central question: How could we select the complexity and the structure of the model to ensure the optimum knowledge gained or the best answer to the question posed by the model? SELECTION OF MODEL COMPLEXITY AND STRUCTURE New knowledge Very good data Bad data Complexity of the model 26 13

14 8. SELECTION OF MODEL COMPLEXITY AND STRUCTURE Balance between complexity and expectations: 1. Good definition of the problem 2. Good knowledge about the system 3. Right complexity of the model Model is a simplification of real system! => it s impossible to make a model of real ecosystem, => models of some aspects of ecosystem may be made SELECTION OF MODEL COMPLEXITY AND STRUCTURE Selection of complexity and model structure depends on feasibility to aggregate similar state variables the number of variables is reduced to one variable the problem is nonlinear relationships between variables which are going to be aggregated. Aggregation of state variables may reduce the reliability of the model

15 8. SELECTION OF MODEL COMPLEXITY AND STRUCTURE Selection of the complicity must not be random because: It affects the outputs from the model (main product of the modeler) Enough time need to be taken to select right level of complexity