Power-Law Persistence in the Atmosphere: Analysis and Applications

We review recent results on the appearance of long-term persistence in climatic records and their relevance for the evaluation of global climate models and rare events.The persistence can be characterized, for example, by the correlation C(s) of temperature variations separated by s days.We show that, contrary to previous expectations, C(s) decays for large s as a power law, C(s) ~ s^(-gamma). For continental stations, the exponent gamma is always close to 0.7, while for stations on islands gamma is around 0.4. In contrast to the temperature fluctuations, the fluctuations of the rainfall usually cannot be characterized by long-term power-law correlations but rather by pronounced short-term correlations. The universal persistence law for the temperature fluctuations on continental stations represents an ideal (and uncomfortable) test-bed for the state of-the-art global climate models and allows us to evaluate their performance. In addition, the presence of long-term correlations leads to a novel approach for evaluating the statistics of rare events.Comment: 12 pages, 6 included EPS figures, added chapter

Phase Synchronization in Temperature and Precipitation Records

We study phase synchronization between atmospheric variables such as daily mean temperature and daily precipitation records. We find significant phase synchronization between records of Oxford and Vienna as well as between the records of precipitation and temperature in each city. To find the time delay in the synchronization between the records we study the time lag phase synchronization when the records are shifted by a variable time interval of days. We also compare the results of the method with the classical cross-correlation method and find that in certain cases the phase synchronization yields more significant results.Comment: 11 pages including 8 figure

Volatility in atmospheric temperature variability

Using detrended fluctuation analysis (DFA), we study the scaling properties of the volatility time series $V_i=| T_{i+1}-T_i|$ of daily temperatures $T_i$ for ten chosen sites around the globe. We find that the volatility is long range power-law correlated with an e xponent $\gamma$ close to 0.8 for all sites considered here. We use this result to test the scaling performance of several state-of-the art global climate models and find that the models do not reproduce the observed scaling behavior.Comment: 10 pages, 3 figures. Accepted for publication in Physica

Recurrence intervals between earthquakes strongly depend on history

We study the statistics of the recurrence times between earthquakes above a certain magnitude M$in California. We find that the distribution of the recurrence times strongly depends on the previous recurrence time$\tau_0$. As a consequence, the conditional mean recurrence time$\hat \tau(\tau_0)$between two events increases monotonically with$\tau_0$. For$\tau_0$well below the average recurrence time$\ov{\tau}, \hat\tau(\tau_0)$is smaller than$\ov{\tau}$, while for$\tau_0>\ov{\tau}$,$\hat\tau(\tau_0)$is greater than$\ov{\tau}$. Also the mean residual time until the next earthquake does not depend only on the elapsed time, but also strongly on$\tau_0$. The larger$\tau_0$ is, the larger is the mean residual time. The above features should be taken into account in any earthquake prognosis.Comment: 5 pages, 3 figures, submitted to Physica

Comment on "Scaling of atmosphere and ocean temperature correlations in observations and climate models"

In a recent letter [K. Fraedrich and R. Blender, Phys. Rev. Lett. 90, 108501 (2003)], Fraedrich and Blender studied the scaling of atmosphere and ocean temperature. They analyzed the fluctuation functions F(s) ~ s^alpha of monthly temperature records (mostly from grid data) by using the detrended fluctuation analysis (DFA2) and claim that the scaling exponent alpha over the inner continents is equal to 0.5, being characteristic of uncorrelated random sequences. Here we show that this statement is (i) not supported by their own analysis and (ii) disagrees with the analysis of the daily observational data from which the grid monthly data have been derived. We conclude that also for the inner continents, the exponent is between 0.6 and 0.7, similar as for the coastline-stations.Comment: 1 page with 2 figure

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

Volcanic forcing improves Atmosphere-Ocean Coupled General Circulation Model scaling performance

Recent Atmosphere-Ocean Coupled General Circulation Model (AOGCM) simulations of the twentieth century climate, which account for anthropogenic and natural forcings, make it possible to study the origin of long-term temperature correlations found in the observed records. We study ensemble experiments performed with the NCAR PCM for 10 different historical scenarios, including no forcings, greenhouse gas, sulfate aerosol, ozone, solar, volcanic forcing and various combinations, such as it natural, anthropogenic and all forcings. We compare the scaling exponents characterizing the long-term correlations of the observed and simulated model data for 16 representative land stations and 16 sites in the Atlantic Ocean for these scenarios. We find that inclusion of volcanic forcing in the AOGCM considerably improves the PCM scaling behavior. The scenarios containing volcanic forcing are able to reproduce quite well the observed scaling exponents for the land with exponents around 0.65 independent of the station distance from the ocean. For the Atlantic Ocean, scenarios with the volcanic forcing slightly underestimate the observed persistence exhibiting an average exponent 0.74 instead of 0.85 for reconstructed data.Comment: 4 figure

Ising-like dynamics and frozen states in systems of ultrafine magnetic particles

We use Monte-Carlo simulations to study aging phenomena and the occurence of spinglass phases in systems of single-domain ferromagnetic nanoparticles under the combined influence of dipolar interaction and anisotropy energy, for different combinations of positional and orientational disorder. We find that the magnetic moments oriente themselves preferably parallel to their anisotropy axes and changes of the total magnetization are solely achieved by 180 degree flips of the magnetic moments, as in Ising systems. Since the dipolar interaction favorizes the formation of antiparallel chain-like structures, antiparallel chain-like patterns are frozen in at low temperatures, leading to aging phenomena characteristic for spin-glasses. Contrary to the intuition, these aging effects are more pronounced in ordered than in disordered structures.Comment: 5 pages, 6 figures. to appear in Phys. Rev.