|
|
Similarities in chaotic behavior of Lorenz 05 model and ECMWF models
Bednář, Hynek ; Raidl, Aleš (advisor) ; Jaňour, Zbyněk (referee) ; Pokorný, Pavel (referee)
This thesis tests the ability of the Lorenz's (2005) chaotic model to simulate predictability curve of the ECMWF model calculated from data over the 1986 to 2011 period and demonstrates similarity of the predictability curves for the Lorenz's model with N = 90 variables. This thesis also tests approximations of predictability curves and their differentials, aiming to correct the ECMWF model estimated parameters and thus allow for estimation of the largest Lyapunov exponent, model error and limit value of the predictability curve. The correction is based on comparing the parameters estimated for the Lorenz's and ECMWF and on comparison with the largest Lyapunov exponent (λ=0,35 day-1 ) and limit value of the predictability curve (E∞=8,2) of the Lorenz's model. Parameters are calculated from approximations made by the Quadratic hypothesis with and without model error, as well as by Logarithmic and General hypotheses and by hyperbolic tangent employing corrections with and without model error. Average value of the largest Lyapunov exponent is estimated to be λ=0,37 day-1 for the ECMWF model, limit values of the predictability curves are estimated with lower theoretically derived values and new approach of calculation of model error based on comparison of models is presented.
|
|
| |
|
|
Chaotic system modeling using MATLAB
Lejdar, Lukáš ; Raidl, Aleš (advisor) ; Šindelářová, Kateřina (referee)
In the presented bachelor's thesis we study behavior of dynamical systems. Some interesting attributes of dynamical systems are presented using programs written by the author. For computational part of the programs MATLAB was used and for presentation of output data MATLAB in combination with GNUPLOT were used. Basic terms in chaos theory are explained with examples. In one-dimensional case we focus on the logistic map and we demonstrate a transition to chaos on it. In two-dimensional space we study the Hénon map and in three-dimensional space we take a closer look at some interesting attributes of the famous Lorenz system.
|
|
| |
|
|
Nonlinear modelling of meteorological data
Pop, Lukáš ; Raidl, Aleš (advisor) ; Mikšovský, Jiří (referee)
Thesis deals with possibilities of application of nonlinear methods based on the theory of dynamical systems, for meteorological problems. In the first part there is explored description of the dynamical systems, namely deterministic chaotic systems, for them this methods were introduced. There is described the concept of attractor and its typical invariants. In the next part there are summarized different ways of reconstruction of phase space of system by means of time series produced by it. A modification of Cao's method is proposed here. Possibilities of prediction of meteorological quantities are proposed here. In the next part there is described influence of different sorts of signal noise and inaccuracies of measuring to the dynamical system that is described by logistic equation. That is a simple example of deterministic chaotic system. In the last part there are analysed single types of errors, of them nonlinear methods of prediction are encumbered. There are described typical properties and specialities of meteorological data. There are tried modifications of local linear models also, what is applied to data of NCEP/NCAR reanalysis.
|
|
| |
|
| |
|
|
Similarities in chaotic behavior of Lorenz 05 model and ECMWF models
Bednář, Hynek ; Raidl, Aleš (advisor) ; Jaňour, Zbyněk (referee) ; Pokorný, Pavel (referee)
This thesis tests the ability of the Lorenz's (2005) chaotic model to simulate predictability curve of the ECMWF model calculated from data over the 1986 to 2011 period and demonstrates similarity of the predictability curves for the Lorenz's model with N = 90 variables. This thesis also tests approximations of predictability curves and their differentials, aiming to correct the ECMWF model estimated parameters and thus allow for estimation of the largest Lyapunov exponent, model error and limit value of the predictability curve. The correction is based on comparing the parameters estimated for the Lorenz's and ECMWF and on comparison with the largest Lyapunov exponent (λ=0,35 day-1 ) and limit value of the predictability curve (E∞=8,2) of the Lorenz's model. Parameters are calculated from approximations made by the Quadratic hypothesis with and without model error, as well as by Logarithmic and General hypotheses and by hyperbolic tangent employing corrections with and without model error. Average value of the largest Lyapunov exponent is estimated to be λ=0,37 day-1 for the ECMWF model, limit values of the predictability curves are estimated with lower theoretically derived values and new approach of calculation of model error based on comparison of models is presented.
|
|
| |
|
|
Manifestation of chaotic behavior in observed and simulated series of climatic variables
Skořepa, Jan ; Mikšovský, Jiří (advisor) ; Raidl, Aleš (referee)
Diplomová práce se věnuje analýze chaotického chování v řadách (pseudo)pozorovaných a simulovaných klimatických veličin. Nejprve objasňuji ně- které základní teoretické pojmy související s dynamickými systémy. Potom se zabývám zp·soby rekonstrukce fázového prostoru a uvedu metody odhadu kore- lační dimenze a největšího Ljapunovova exponentu. V praktické části se zabývám pr·měrnou denní teplotou z reanalýz ERA-40 a reanalýzami NCEP/NCAR v tlakových hladinách 850 a 500 hPa z let 1960-2000. Nejprve zkoumám podrobně jednu vybranou řadu. Používám např. metodu falešných soused· a určuji míru vzájemné informace. Zjiš'uji, že korelační dimenze nenabývá konkrétní hodnotu. Pro analýzu celých tlakových hladin vyvíjím program, který počítá divergenci blízkých trajektorií, což je postup používaný při výpočtu největšího Ljapunovo- va exponentu. Tento program postupně aplikuji na oblasti velikosti 20◦ × 30◦ kterými je pokryta celá zeměkoule. Postupně ukazuji a srovnávám výsledky pro reanalýzy v obou tlakových hladinách s ročním chodem a odečteným ročním cho- dem. Tuto metodu aplikuji na výstupy globálních klimatických model· HadCM3 a MPI-ESM-MR v hladině 500 hPa. Podobnou analýzu ještě uskutečňuji u jed- nodimenzionálních řad teploty u reanalýz a u model·. Výsledky opět vizuálně srovnávám. 1
|
guest ::
