MPI 794 (week-1 & 2)
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The document discusses the principles of climate modeling, emphasizing the difference between classical and non-classical methods, including data-driven modeling and artificial intelligence. It outlines the importance of accurate modeling for understanding climate systems and predicting future climates, while also noting the challenges and uncertainties associated with modeling due to simplifications and human activities. Additionally, various applications and tools for numerical modeling in climate science are presented.
MPI 794 (week-1 & 2)
- 1. Yasser B. A. Farag MSc. of Maritime Energy Management – WMU - Sweden Lecturer at Institute of Maritime Upgrading Studies Maritime Chief Engineer Maritime Postgraduate Institute - 2 0 2 0 - Numerical Modeling & tools MPI 794
- 2. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 Contents • Background & Introduction • Classical vs Non-classical methods • Data-driven modelling • Artificial intelligence (AI) • Case study (using an Artificial Neural Network-ANN) 2
- 3. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 The need 3 Climate models are tools employed to enhance understanding of the climate system and to aid prediction of future climates. Although there have been great advances made in the discipline of climate modelling over its forty year history, even the most sophisticated models remain very much simpler than the full climate system.
- 4. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 Origin 4 www.AMNH.org
- 5. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 Background 5 Greenhouse effect schematic showing energy flows between space, the atmosphere, and Earth's surface. Energy influx and emittance are expressed in watts per square meter(W/m2). A greenhouse gas is a gas in an atmosphere that absorbs and emits radiant energy within the thermal infrared range. This process is the fundamental cause of the greenhouse effect. The primary greenhouse gases in Earth's atmosphere are water vapor, carbon dioxide, methane, nitrous oxide, and ozone. Without greenhouse gases, the average temperature of Earth's surface would be about −18 °C rather than the present average of 15 °C. Human activities since the beginning of the Industrial Revolution (around 1750) have produced a 40% increase in the atmospheric concentration of carbon dioxide (CO2), from 280 ppm in 1750 to 406 ppm in early 2017 https://nems.nih.gov
- 6. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 Understanding 6 Human activities since the beginning of the Industrial Revolution (around 1750) have produced a 40% increase in the atmospheric concentration of carbon dioxide (CO2), from 280 ppm in 1750 to 409 ppm in 2019 (NASA simulation)
- 7. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 Understanding 7 (NASA simulation) Source: Global Carbon budget
- 8. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 Understanding 8
- 9. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 Prediction 9
- 10. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 Modeling 10 • Most real-word applications lead to mathematical problems which cannot be solved with exact formulas, or analytically • A common approach is to reduce a problem to special cases and simplified situations, and study those in detail • The aim is to uncover generally applicable concepts and properties, which can guide us in more difficult problems
- 11. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 Modeling 11 • The simplified analytical model (e.g., set of equations) for problem is converted into a numerical model Can be solved in a finite number of basic arithmetic operations Approximation of an analytical model (error) • A numerical model is solved with numerical methods, introducing additional errors • Machine representation: computers have a limit on how small or large a number can be
- 12. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 Simulation 12 • Simulation is the representation of the behavior or characteristics of one system through the use of another system, especially a computer program designed for the purpose. • A model is a simplified representation of a system or phenomenon with any hypotheses required to describe the system or explain the phenomenon.
- 13. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 Conceptual Models 13 • Depending on the type of description of reality, models can be classified as conceptual or mathematical. • A conceptual model is a qualitative description of “some aspect of the behavior of a natural system.” • This description is usually verbal, but can also be accompanied by pictures and graphics. 𝒗 𝒔 Wind Waves Current Swirl Water depth Draught & Trim Loading condition Hull fouling Propeller condition Thrust Fuel Engine condition
- 14. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 Mathematical Models 14 • A mathematical model is a summary description (summary in the sense that it is based on variables, equations and so on) of “some aspect of the behavior of a natural system”. However, the motivation of mathematical models is not abstraction but quantification. • Mathematical modeling methods (discretization, calibration, etc.) are more specific. However, it should be clear that the conceptualization is the first step in modeling and mathematical modeling helps in building strong conceptual models.
- 15. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 Model types 15 Depending on how to solve the equations, the models can be classified into analytical and numerical. Model Physical Static Dynamic Mathematical Static Numerical Analytical Dynamic Analytical Numerical Simulation
- 16. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 Analytical vs numerical models 16 • The analytical models are based on closed structure solutions, they are convenient because they are easy to evaluate and intuitive (a look at the equation can give an idea of the phenomenon). As a result, they are used very often. • Numerical models are based on partial differential equations which regulate the natural phenomenon. This leads to linear systems of equations can be solved only with the help of a computer. • The advantage of numerical models is its generality. Analytical models are limited to homogeneous domains, the simple geometry and boundary conditions. Numerical models, on the other hand, can handle spatially and temporally variable properties, arbitrary geometry and boundary conditions and processes. The price to pay is the methodological uniqueness. Analytical models are easy to use. Numerical models can be complex and often difficult. • Also, it should be distinguished between specific models and generic models. The former is for a specific place, while the latter emphasize processes, regardless of where it is performed.
- 17. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 Analytical vs numerical models 17 • Models are often used as decision support tools. Building an accurate model is very difficult and takes time. As a result, rarely can you expect models that generate accurate predictions. However, approximate models are much easier to build. They do not lead to accurate predictions, but usually allow a reasonable assessment of the results of different management alternatives. That is, you can evaluate the relevant advantages and disadvantages of each alternative and rank the options. This is usually all that is needed for decision-making.
- 18. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 MODELING PROCESS 18 • The procedure for constructing a model is as follows. First, a conceptual model. Secondly, the model is discretized. This can be entered as input data for a simulation code. Unfortunately, the output data rarely conform to the observations. This is what leads to the calibration, i.e., modifying model parameters to ensure that the output of the model is similar to that observed in reality. Therefore, the calibrated model may be considered as a “representation of the natural system” and can be used for management purposes or simulation. • CONCEPTUALIZATION: Modeling begins by defining what processes are important and how they are represented in the model. A definition of the relevant processes is called “identification process” and is necessary for several reasons. First, the number of processes that may affect is very large. For practical reasons, the designer is forced to select those that most significantly affect the phenomenon under study. Second, not all processes are well understood and must be treated in a simplified manner. Briefly, the process involves identification simplifications in the choice thereof as in the way they are implemented in the model. The identification of the structure of the model refers to the definition of the variability of parameters, boundary conditions, etc. In a somewhat smaller but more systematic way, identifying the model structure involves expressing the model in terms of a finite number of unknowns called model parameters. The parameters that control the above processes are variable in space and, in some cases, they can also vary in time. The data are usually limited, so variability cannot be expressed accurately. Therefore, the designer is also forced to make many simplifications to express patterns of variation in parameters, boundary conditions, etc. These assumptions are reflected in the model’s structure. The conceptualization of any modeling is subjective and depends on the ingenuity of the modeler, experience, scientific knowledge, and how to look at the data.
- 19. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 MODELING PROCESS 19 • DISCRETIZATION: is to replace a continuum with a discrete system. Yet here we are extending this term to describe the process of moving from mathematical equations derived from the conceptual model to numerical expressions which can be solved by a computer. Closely related is the issue of verification, which is to ensure that a code solves the equations accurately. As such, verification is a concept that dependents on the code.
- 20. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 MODELING PROCESS 20 • MODEL SELECTION The first step in any modeling effort is the construction of a conceptual model, describing through appropriate regulatory equations, and lastly translating to computer code. Model selection process involves choosing between types of alternative models. The methods for selecting the model can be classified into three broad categories. The first category is based on a comparative analysis of the residuals (differences between measured and calculated responses of the system) using both objective and subjective criteria. In the second category there is the selection of parameters, and it consists in evaluating whether the calculated parameters may be considered “reasonable”. The third category is based on theoretical model validity measures known as “identification criteria”. In practice, the three categories are required: residue analysis and evaluation of the parameters suggest ways to modify an existing model, and the consequent improvement in the realization of the model is evaluated on the basis of criteria of identification. If the modified model is considered an improvement over the previous model, the modified is accepted and the previous discarded.
- 21. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 PREDICTIONS AN UNCERTAINTY 21 • Most of the models are created in order to study the response of the environment to several alternative scenarios. Very often, you stress the scenario in a way that the model structure is not valid any more. • Also, uncertainty about future natural and human-induced stresses cause the model predictions to be uncertain. • Finally, even if future conditions and the conceptual model were known exactly, errors in the model parameters still produce errors in predictions.
- 22. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 PREDICTIONS AN UNCERTAINTY 22 • Most real-word applications lead to mathematical problems which cannot be solved with exact formulas, or analytically • A common approach is to reduce a problem to special cases and simplified situations, and study those in detail • Errors accumulate through every simplification step at the model level, and at every approximation related to model implementation
- 23. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 Applications 23 • Finite Element Analysis (FEA)
- 24. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 Applications 24 • Computational Fluid Dynamic - CFD
- 25. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 Applications 25 • Climate modeling
- 26. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 Applications 26 • Data modeling
- 27. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 Applications 27
- 28. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 Tools 28 • ANSYS
- 29. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 Tools 29 • SPSS
- 30. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 Tools 30 • Even Excel!
- 31. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 Tools 31 • Python
- 32. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 Tools 32 • MATLAB MATLAB is a proprietary multi-paradigm programming language and numerical computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.
- 33. MPI Climate Change N u m e r i c a l m o d e l i n g & t o o l s M P I 7 9 4 | Y A S S E R B . A . F A R A G6 December 2020 Tools 33 • FORTRAN is a general-purpose, compiled imperative programming language that is especially suited to numeric computation and scientific computing.