Power-law persistence and trends in the atmosphere: A detailed study of long temperature records

We use several variants of the detrended fluctuation analysis to study the appearance of long-term persistence in temperature records, obtained at 95 stations all over the globe. Our results basically confirm earlier studies. We find that the persistence, characterized by the correlation C(s) of temperature variations separated by s days, decays for large s as a power law, C(s) ~ s^(-gamma). For continental stations, including stations along the coastlines, we find that gamma is always close to 0.7. For stations on islands, we find that gamma ranges between 0.3 and 0.7, with a maximum at gamma = 0.4. This is consistent with earlier studies of the persistence in sea surface temperature records where gamma is close to 0.4. In all cases, the exponent gamma does not depend on the distance of the stations to the continental coastlines. By varying the degree of detrending in the fluctuation analysis we obtain also information about trends in the temperature records.Comment: 5 pages, 4 including eps figure

Percolation of randomly distributed growing clusters: Finite Size Scaling and Critical Exponents

We study the percolation properties of the growing clusters model. In this model, a number of seeds placed on random locations on a lattice are allowed to grow with a constant velocity to form clusters. When two or more clusters eventually touch each other they immediately stop their growth. The model exhibits a discontinuous transition for very low values of the seed concentration $p$ and a second, non-trivial continuous phase transition for intermediate $p$ values. Here we study in detail this continuous transition that separates a phase of finite clusters from a phase characterized by the presence of a giant component. Using finite size scaling and large scale Monte Carlo simulations we determine the value of the percolation threshold where the giant component first appears, and the critical exponents that characterize the transition. We find that the transition belongs to a different universality class from the standard percolation transition.Comment: 5 two-column pages, 6 figure

Critical dimensions for random walks on random-walk chains

The probability distribution of random walks on linear structures generated by random walks in $d$-dimensional space, $P_d(r,t)$, is analytically studied for the case $\xi\equiv r/t^{1/4}\ll1$. It is shown to obey the scaling form $P_d(r,t)=\rho(r) t^{-1/2} \xi^{-2} f_d(\xi)$, where $\rho(r)\sim r^{2-d}$ is the density of the chain. Expanding $f_d(\xi)$ in powers of $\xi$, we find that there exists an infinite hierarchy of critical dimensions, $d_c=2,6,10,\ldots$, each one characterized by a logarithmic correction in $f_d(\xi)$. Namely, for $d=2$, $f_2(\xi)\simeq a_2\xi^2\ln\xi+b_2\xi^2$; for $3\le d\le 5$, $f_d(\xi)\simeq a_d\xi^2+b_d\xi^d$; for $d=6$, $f_6(\xi)\simeq a_6\xi^2+b_6\xi^6\ln\xi$; for $7\le d\le 9$, $f_d(\xi)\simeq a_d\xi^2+b_d\xi^6+c_d\xi^d$; for $d=10$, $f_{10}(\xi)\simeq a_{10}\xi^2+b_{10}\xi^6+c_{10}\xi^{10}\ln\xi$, {\it etc.\/} In particular, for $d=2$, this implies that the temporal dependence of the probability density of being close to the origin $Q_2(r,t)\equiv P_2(r,t)/\rho(r)\simeq t^{-1/2}\ln t$.Comment: LATeX, 10 pages, no figures submitted for publication in PR

Global climate models violate scaling of the observed atmospheric variability

We test the scaling performance of seven leading global climate models by using detrended fluctuation analysis. We analyse temperature records of six representative sites around the globe simulated by the models, for two different scenarios: (i) with greenhouse gas forcing only and (ii) with greenhouse gas plus aerosol forcing. We find that the simulated records for both scenarios fail to reproduce the universal scaling behavior of the observed records, and display wide performance differences. The deviations from the scaling behavior are more pronounced in the first scenario, where also the trends are clearly overestimated.Comment: Accepted for publishing in Physical Review Letter

Detrended fluctuation analysis as a statistical tool to monitor the climate

Detrended fluctuation analysis is used to investigate power law relationship between the monthly averages of the maximum daily temperatures for different locations in the western US. On the map created by the power law exponents, we can distinguish different geographical regions with different power law exponents. When the power law exponents obtained from the detrended fluctuation analysis are plotted versus the standard deviation of the temperature fluctuations, we observe different data points belonging to the different climates, hence indicating that by observing the long-time trends in the fluctuations of temperature we can distinguish between different climates.Comment: 8 pages, 4 figures, submitted to JSTA

Probing non-Gaussianities in the CMB on an incomplete sky using surrogates

We demonstrate the feasibility to generate surrogates by Fourier-based methods for an incomplete data set. This is performed for the case of a CMB analysis, where astrophysical foreground emission, mainly present in the Galactic plane, is a major challenge. The shuffling of the Fourier phases for generating surrogates is now enabled by transforming the spherical harmonics into a new set of basis functions that are orthonormal on the cut sky. The results show that non-Gaussianities and hemispherical asymmetries in the CMB as identified in several former investigations, can still be detected even when the complete Galactic plane (|b| < 30{\deg}) is removed. We conclude that the Galactic plane cannot be the dominant source for these anomalies. The results point towards a violation of statistical isotropy.Comment: 9 pages, 13 figures, accepted by Physical Review

Invaded cluster algorithm for a tricritical point in a diluted Potts model

The invaded cluster approach is extended to 2D Potts model with annealed vacancies by using the random-cluster representation. Geometrical arguments are used to propose the algorithm which converges to the tricritical point in the two-dimensional parameter space spanned by temperature and the chemical potential of vacancies. The tricritical point is identified as a simultaneous onset of the percolation of a Fortuin-Kasteleyn cluster and of a percolation of "geometrical disorder cluster". The location of the tricritical point and the concentration of vacancies for q = 1, 2, 3 are found to be in good agreement with the best known results. Scaling properties of the percolating scaling cluster and related critical exponents are also presented.Comment: 8 pages, 5 figure

Self-Organized Dynamical Equilibrium in the Corrosion of Random Solids

Self-organized criticality is characterized by power law correlations in the non-equilibrium steady state of externally driven systems. A dynamical system proposed here self-organizes itself to a critical state with no characteristic size at ``dynamical equilibrium''. The system is a random solid in contact with an aqueous solution and the dynamics is the chemical reaction of corrosion or dissolution of the solid in the solution. The initial difference in chemical potential at the solid-liquid interface provides the driving force. During time evolution, the system undergoes two transitions, roughening and anti-percolation. Finally, the system evolves to a dynamical equilibrium state characterized by constant chemical potential and average cluster size. The cluster size distribution exhibits power law at the final equilibrium state.Comment: 11 pages, 5 figure