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An Introduction to Complex Systems in Environment
Thu, 13 Apr 2017 22:00:00 GMT
The environment is a social issue that continues to grow in importance. Its complexity, both crossdisciplinary and multiscale, has given rise to a large number of scientific and technological locks, that can be solved using a complex systems approaches. Through this courses we will give some examples of complex systems that can be found in environment and their observable, we will highlight the variability of these fields over a wide range of scales. We will focus on the fractal/multifractal behaviour of the environnemental fields and introduce some tools that allow us to charchterize their spatial/temporal variability. The courses is devided in 11 modules as follows:
Introduction
Source of Complexity
Dynamical Systems
Cascade Phenomenology
Spectral Analysis
MultiScale Analysis: Fractal
MultiScale Analysis :Multifractal
Multiscale Analysis: Methods of Analysis
MultiScale Simulations
Extremes
Resilience
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Extremes (An Introduction to Complex Systems in Environment)
Thu, 13 Apr 2017 22:00:00 GMT
The extreme value theory deals with the stochastic behavior of the minimum and the maximum of random variable. It involves a large variety of applications such as natural phenomena: rainfall, floods, atmospheric turbulence, corrosion...etc. The distribution proprieties of extremes and intermediate order statistics are determined by the upper and lower tails of the probability distribution.
Module 10 of the course set "An Introduction to Complex Systems in Environment"
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Multiscale Analysis: Methods of Analysis (An Introduction to Complex Systems in Environment)
Thu, 13 Apr 2017 22:00:00 GMT
We gave in the courses Multifractal the meaning of the universal multifractal (UM) parameters and , in this courses we will introduce some techniques of estimation of UM parameters based on the scale invariance property of geophysical fields. The first method is the Trace Moment (TM) method which uses the allows to estimate the statistical moment function in the first step and after that to estimate the UM parameters either by the geometrical characteristic of the function or by its mathematical proprieties. The second method, called the Double Trace Moment which is a generalization of the TM method will be introduced and some of its characteristics will be highlighted. We introduce also the Structure Function Analysis which allows us to study the statistics of a non conservative field and estimate the different scaling exponent. In this courses we will also introduce the Empirical Modal Decomposition in order to separate the effects of large scale on the smallest one, which can affect the estimation of the UM parameters.
Module 8 of the course set "An Introduction to Complex Systems in Environment"
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MultiScale Analysis :Multifractal (An Introduction to Complex Systems in Environment)
Thu, 13 Apr 2017 22:00:00 GMT
The multifractal analysis is an appropriate framework for addressing and modelling fields with high spatial and temporal variability, particularly with regard to the characteristics of nonuniformity of the phenomena and their extreme behavior. Therefore, the idea of applying this concepts to the description of geophysical variables came naturally to mind scientists.
There exist different areas of application : geology, meteorology, hydrology, biology, geomorphology, topography...., etc.
Module 7of the course set "An Introduction to Complex Systems in Environment"
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MultiScale Simulations (An Introduction to Complex Systems in Environment)
Thu, 13 Apr 2017 22:00:00 GMT
We have seen during the previous lecture the concept of cascade phenomenology and the different models that can be found in the literature. It has been showed the cascade generation is based on the scale invariance propriety and the multiplicative process. The use of simulation is increasingly common in environmental field because it allows us to access to information at small scale and to have a detailed description and understanding of the process.
In the stochastic simulation we simulate the evolution of variables that can change stochastically (randomly) with certain probabilities. We will show in this lecture some of techniques to simulate (generate) some stochastic fields according to some probability distribution. We focus on the multifractal simulation tp show how can we generate a multiscale (conservative and nonconservative) field . We finished with two exercises in order to practice the different techniques.
Module 9 of the course set "An Introduction to Complex Systems in Environment"
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