Estimating the Fractal Dimension, K_2-entropy, and the Predictability of the Atmosphere

The series of mean daily temperature of air recorded over a period of 215 years is used for analysing the dimensionality and the predictability of the atmospheric system. The total number of data points of the series is 78527. Other 37 versions of the original series are generated, including ``seasonally adjusted'' data, a smoothed series, series without annual course, etc. Modified methods of Grassberger and Procaccia are applied. A procedure for selection of the ``meaningful'' scaling region is proposed. Several scaling regions are revealed in the ln C(r) versus ln r diagram. The first one in the range of larger ln r has a gradual slope and the second one in the range of intermediate ln r has a fast slope. Other two regions are settled in the range of small ln r. The results lead us to claim that the series arises from the activity of at least two subsystems. The first subsystem is low-dimensional (d_f=1.6) and it possesses the potential predictability of several weeks. We suggest that this subsystem is connected with seasonal variability of weather. The second subsystem is high-dimensional (d_f>17) and its error-doubling time is about 4-7 days. It is found that the predictability differs in dependence on season. The predictability time for summer, winter and the entire year (T_2 approx. 4.7 days) is longer than for transition-seasons (T_2 approx. 4.0 days for spring, T_2 approx. 3.6 days for autumn). The role of random noise and the number of data points are discussed. It is shown that a 15-year-long daily temperature series is not sufficient for reliable estimations based on Grassberger and Procaccia algorithms.Comment: 27 pages (LaTex version 2.09) and 15 figures as .ps files, e-mail: [email protected]

Time Evolution of Initial Errors in Lorenz's 05 Chaotic Model

Initial errors in weather prediction grow in time and, as they become larger, their growth slows down and then stops at an asymptotic value. Time of reaching this saturation point represents the limit of predictability. This paper studies the asymptotic values and time limits in a chaotic atmospheric model for five initial errors, using ensemble prediction method (model's data) as well as error approximation by quadratic and logarithmic hypothesis and their modifications. We show that modified hypotheses approximate the model's time limits better, but not without serious disadvantages. We demonstrate how hypotheses can be further improved to achieve better match of time limits with the model. We also show that quadratic hypothesis approximates the model's asymptotic value best and that, after improvement, it also approximates the model's time limits better for almost all initial errors and time lengths

Time Evolution of Initial Errors in Lorenz’s 05 Chaotic Model

Initial errors in weather prediction grow in time and, as they become larger, their growth slows down and then stops at an asymptotic value. Time of reaching this saturation point represents the limit of predictability. This paper studies the asymptotic values and time limits in a chaotic atmospheric model for five initial errors, using ensemble prediction method (model’s data) as well as error approximation by quadratic and logarithmic hypothesis and their modifications. We show that modified hypotheses approximate the model’s time limits better, but not without serious disadvantages. We demonstrate how hypotheses can be further improved to achieve better match of time limits with the model. We also show that quadratic hypothesis approximates the model’s asymptotic value best and that, after improvement, it also approximates the model’s time limits better for almost all initial errors and time lengths

Odhady rozsahu změn klimatu České republiky pro tři časová období 21. století na základě výstupů AR4 modelů

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Atlas podnebí České republiky a regionalizace výstupů modelů všeobecné cirkulace atmosféry pro potřeby území České republiky

Cílem projektu je vyhotovení Atlasu podnebí České republiky za standardní klimatologické období 1961-90, zpracování hlavních klimatických prvků za období 1961-1990 do mapových podkladů ČR v digitální formě, regionalizace výstupů klimatických modelů nelineárními metodami pro potřeby území České republiky a jejich porovnání s lineárními postupy. Zpráva je rozdělena do dvou dílčích projektů: Atlas podnebí ČR a Regionalizace výstupů modelů všeobecné cirkulace atmosféry pro potřeby území České republiky (lineárními a nelineárnímu metodami)

Atlas podnebí České republiky a regionalizace výstupů modelů všeobecné cirkulace atmosféry pro potřeby území České republiky:Regionalizace výstupů modelů všeobecné cirkulace atmosféry pro potřeby území České republiky

Cílem dílčího projektu 02 je posoudit možnosti regionalizace výstupů klimatických modelů nelineárními metodami pro potřeby území České republiky a jejich porovnání s lineárními postupy. Dílčí projekt je rozdělený do dvou částí: regionalizace výstupů globálních klimatických modelů lineárními metodami a regionalizace výstupů globálních klimatických modelů lineárními metodami