1 Enviromatics Environmental simulation models Environmental simulation models Вонр. проф. д-р Александар Маркоски Технички факултет – Битола 2008 год.

2 Enviromatics Environmental simulation models Introduction Environmental models describe and quantify the behaviour of an environmental system. There are two ways of environmental modelling: 1.The experimental statistical modelling or 2.the dynamic modelling procedure.

3 Enviromatics Environmental simulation models Comparison of black-box (statistical) and dynamic approach of ecosystem modelling

4 Enviromatics Environmental simulation models Comparison of black-box and dynamic approach of ecosystem modelling (2)

5 Enviromatics Environmental simulation models Models Compartment-oriented models and individual-oriented models will be distinguished. Process models simulate environmental processes. Observations and measurements taken from environmental monitoring and laboratory investigations serve as inputs to such models. Then various scenarios of environmental behaviour will be computed with different parameter sets. \ Besides improving the overall economic efficiency of a process, a parameter optimisation may have positive consequences with regard to the environment.

6 Enviromatics Environmental simulation models Models (2) In principle, there are no differences between mathematical models of environmental systems and mathematical models of environmental processes, which are used as elements in such models. Environmental systems are multidimensional systems with several input and output variables. Their models may be distinguished by static models (black box models, input- output models) or dynamic models. In dependence of the number of input variables and the number of output variables SIMO-, MIMO-, SISO- and MISO-systems will be distinguished for black box models. Environmental processes might be described by using more or less details.

7 Enviromatics Environmental simulation models Modelling procedure Modelling and simulation are important analysis tools in a variety of scientific and practical disciplines. The construction and application of mathematical models are primary problems in environmental systems analysis. Any mathematical model which enables better understanding of a given problem is just as important as observations and facts. A mathematical model is an abstract description of a real-life phenomenon. A mathematical model is never identical with reality but it rather constitutes our own fiction. The abstraction usually involves some simplification and results in a formal representation. The model provides for a reduction of redundancy and acts as a link between theoretical and empirical cognition. Abstraction is the basis of systems analysis, which reveals the major characteristic of a mathematical model. Any theory about the course of events in nature is necessarily based on simplification.

8 Enviromatics Environmental simulation models

9 Model testing and analysis Relations between the major state variables of a given model will usually not be in full congruence with the relations between state variables in a real environmental system. Reality must be distorted (error of relations). A real systemmodel comparison can now be made for error assessment which is continued until the model is in sufficient agreement with the real system. Such a model testing leads to an improvement of the verbal and/or mathematical model or to an accumulation of wider knowledge on the real system and can be repeated several times. Once a mathematical model is tested it may be applied also to other states of the same system or even to systems which had not directly been subjects of the study at hand. This approach is defined as prediction. The utilisation of models to enhance our own theoretical and experimental knowledge is defined as model analysis, an approach which has only recently aroused greater attention in the context of theoretical models. The model is used to undertake simulation experiments as tools with which to find answers to specific questions.

10 Enviromatics Environmental simulation models Types and classification of mathematical models Mathematical models are used as substitutes for real processes and systems, but in their behaviour they should be comparable to real objects. Hence, any modelling means a compromise between theory and experiment.

11 Enviromatics Environmental simulation models Transport models Transport models simulate the migration of substances in water, atmosphere and soil. They start from assumptions about the emissions and conditions of transport and make predictions about the emissions at particular locations. They serve as powerful informatic tools to forecast environmental loads resulting from some kind of intended or unintended anthropogenic action. They can also be used in an inverse manner. Two types of transport models may be distinguished. Eulerian models rely on grid-based computations, while Lagrangian models consider single particles.

12 Enviromatics Environmental simulation models Resource utilisation models Resource utilisation models take into account a broader variety of related phenomena than transportation models. They require the consideration of internal and external driving forces and anthropogenic interactions. In particular, for groundwater and surface water systems a lot of mathematical models like selfpurification and eutrophication models exist which describe changes of water quantity and quality. They are used for water management of river basins.

13 Enviromatics Environmental simulation models Process of knowledge acquisition In the process of knowledge acquisition a compilation of a preliminary mathematical model from experience originating from observations and reflections as well as from evaluation of literature has to be made. On top of experience a preliminary model has room for speculation. Then, the preliminary model has to be transformed into a formalised hypothesis and checkable conclusions from the hypothesis should be derived. The validity of these conclusions has to be checked by data not used in the formulation of the hypothesis. If the conclusions prove to be correct, the cognitive process can be continued, otherwise start the knowledge acquisition process again.

14 Enviromatics Environmental simulation models Different classifications of mathematical simulation models Different classifications of mathematical simulation models are known. Mathematical models may be classified by their major properties: Generality, reality or precision. Class 1 covers models in which generality is neglect in favour of reality and precision. Included in class 2 are models which are realistic and general but less precise. In class 3 the model reality is suppressed in favour of generality and precision. Other classifications are given by system dynamics, by the kind of mathematical description, by data availability, or by the type of parameters used.

15 Enviromatics Environmental simulation models Example: