DYNAMICS FLUCTUATIONS IN FINITE SPATIAL AND TEMPORAL NON-LINEAR SYSTEMS AND THEIR APPLICATION IN WEATHER FORECASTING TO PROBABILISTICA BY JOINT.Author:
PRIMO RAMOS CRISTINA.
Year:
2005.
University:
CANTABRIA [
www.unican.es].
Place of defense: E.T.S.DE INGENIEROS DE CAMINOS, C.Y P..
Place of preparation: ESCUELA TECNICA SUPERIOR DE INGENIEROS DE CAMINOS, CANALES Y PUERTOS.
Summary: This thesis examines the problem of predictability of chaotic systems space. This problem is of great interest at present, as shown in numerous practical problems (including weather forecasting term average seasonal and climatic conditions) and are not available ningunan general theory for treatment. This analysis will be conducted from the perspective of dynamic scaling of surfaces, which is a theory consolidated. To do so, I will establish an analogy between the 'surface' generated by fluctuations caused by an error initial, and a rough interface. This analogy is made possible by a transformation into space logarítmic, to be a constant throughout the thesis. This idea has been suggested because fluctuations chaotic grow exponentially. The analysis proposes the idea that the logarithm of erores grows in the same way that a rough interface. Using then the theories of dynamic scaling of rough surfaces are able to rigorously define the dynamics of spatial correlation. Furthermore, the traditional analysis of Liapunov defines some exponents of growth that characterize the system. In systems with few degrees of freedom, this is enough pra a complete characterization, but in space systems, a long list of positive and negative exponents does not help to understand the processes of growth of mistakes, even more so if we take into account also its non-linear character. The classic theory of Liapunov is by definition a linear theory, while the erorres real growing up in non-linear form. Therefore, the proposed method also takes into account the nonlinear effects. Preliminary work undertaken coupled with chaotic systems show that while the evolution of the fluctuations is developed in space tangent (linearized equations) the correlation grows according to the scaling of the interface and descorrelaciona totally nonlinear effects when operating, building developments outside space tangent. Applying laws of scale we can define the whole dynamic process of growth and fluctuations besides controlling its structure. Thus, this work represents a first attempt to characterize the dynamic theoretical space growth of errors. Finally, it will discuss the usefulness of these methods for generating sets of initial conditions in the probabilistic weather prediction, the known method of spreading 'breeding'. This thesis will propose a new method of generating initial conditions, 'breeding logarithmic', which allows to obtain a desired structure space, as well as a characterization of the space evolution of the entire initial disturbance.
