Diego Rybski

Long-term persistence and multifractality of precipitation and river runoff records

[1]xa0We discuss and compare the multifractal temporal scaling properties of precipitation and river discharge records on large timescales. To detect long-term correlations and multifractal behavior in the presence of trends, we apply recently developed methods (detrended fluctuation analysis (DFA) and multifractal DFA) that can systematically detect nonstationarities and overcome trends in the data at all timescales. We find that above some crossover time that usually is several weeks, the daily runoffs are characterized by an asymptotic scaling exponent that indicates a slow power law decay of the runoff autocorrelation function and varies from river to river in a wide range. Below the crossovers, pronounced short-term correlations occur. In contrast, most of the precipitation series show scaling behavior corresponding to a rapid decay of the autocorrelation function. For the multifractal characterization of the data we determine the generalized Hurst exponents and fit them by three operational models. While the fits based on the universal multifractal model describe well the scaling behavior of the positive moments in nearly all runoff and precipitation records, positive as well as negative moments are consistent with two-parameter fits from a modified version of the multiplicative cascade model for all runoff records and most of the precipitation records. For some precipitation records with weak multifractality, however, a simple bifractal characterization gives the best fit of the data.

Laws of population growth

An important issue in the study of cities is defining a metropolitan area, because different definitions affect conclusions regarding the statistical distribution of urban activity. A commonly employed method of defining a metropolitan area is the Metropolitan Statistical Areas (MSAs), based on rules attempting to capture the notion of city as a functional economic region, and it is performed by using experience. The construction of MSAs is a time-consuming process and is typically done only for a subset (a few hundreds) of the most highly populated cities. Here, we introduce a method to designate metropolitan areas, denoted “City Clustering Algorithm” (CCA). The CCA is based on spatial distributions of the population at a fine geographic scale, defining a city beyond the scope of its administrative boundaries. We use the CCA to examine Gibrats law of proportional growth, which postulates that the mean and standard deviation of the growth rate of cities are constant, independent of city size. We find that the mean growth rate of a cluster by utilizing the CCA exhibits deviations from Gibrats law, and that the standard deviation decreases as a power law with respect to the city size. The CCA allows for the study of the underlying process leading to these deviations, which are shown to arise from the existence of long-range spatial correlations in population growth. These results have sociopolitical implications, for example, for the location of new economic development in cities of varied size.

Scaling laws of human interaction activity

Even though people in our contemporary technological society are depending on communication, our understanding of the underlying laws of human communicational behavior continues to be poorly understood. Here we investigate the communication patterns in 2 social Internet communities in search of statistical laws in human interaction activity. This research reveals that human communication networks dynamically follow scaling laws that may also explain the observed trends in economic growth. Specifically, we identify a generalized version of Gibrats law of social activity expressed as a scaling law between the fluctuations in the number of messages sent by members and their level of activity. Gibrats law has been essential in understanding economic growth patterns, yet without an underlying general principle for its origin. We attribute this scaling law to long-term correlation patterns in human activity, which surprisingly span from days to the entire period of the available data of more than 1 year. Further, we provide a mathematical framework that relates the generalized version of Gibrats law to the long-term correlated dynamics, which suggests that the same underlying mechanism could be the source of Gibrats law in economics, ranging from large firms, research and development expenditures, gross domestic product of countries, to city population growth. These findings are also of importance for designing communication networks and for the understanding of the dynamics of social systems in which communication plays a role, such as economic markets and political systems.

Multifractality of river runoff and precipitation: comparison of fluctuation analysis and wavelet methods

We study the multifractal temporal scaling properties of river discharge and precipitation records. We compare the results for the multifractal detrended fluctuation analysis method with the results for the wavelet-transform modulus maxima technique and obtain agreement within the error margins. In contrast to previous studies, we find non-universal behaviour: on long time scales, above a crossover time scale of several weeks, the runoff records are described by fluctuation exponents varying from river to river in a wide range. Similar variations are observed for the precipitation records which exhibit weaker, but still significant multifractality. For all runoff records the type of multifractality is consistent with a modified version of the binomial multifractal model, while several precipitation records seem to require different models.

Long-term persistence in climate and the detection problem

We have analyzed six recently reconstructed records (Jones et al., 1998; Mann et al., 1999; Briffa, 2000; Esper et al., 2002; Mclntyre and McKitrick, 2003; and Moberg et al., 2005) of the Northern Hemisphere temperatures and found that all are governed by long-term persistence. Due to the long-term persistence, the mean temperature variations a(m, L) between L years, obtained from moving averages over m years, are considerably larger than for uncorrelated or short-term correlated records. We compare the values for a(m, L) with the most recent temperature changes ΔT i (m, L) in the corresponding instrumental record and determine the year i c where ΔT i (m, L)/σ(m, L) exceeds a certain threshold and the first year i d when this could be detected. We find, for example, that for the climatologically relevant parameters m = 30, L = 100, and the threshold 2.5, the values (i c , i d ) range, for all records, between (1976, 1990) for Mann et al. (1999) and (1988, 2002) for Jones et al. (1998). Accordingly, the hypothesis that at least part of the recent warming cannot be solely related to natural factors, may be accepted with a very low risk, independently of the database used.

Long‐term memory in 1000‐year simulated temperature records

[1]xa0We study the appearance of long-term persistence in temperature records, obtained from the global coupled general circulation model ECHO-G for two runs, using detrended fluctuation analysis. The first run is a historical simulation for the years 1000–1990 (with greenhouse gas, solar, and volcanic forcing), while the second run is a 1000-year “control run” with constant external forcings. We consider daily data of all grid points as well as their biannual averages in order to suppress 2-year oscillations appearing in the model records for some sites near the equator. Our results substantially confirm earlier studies of (considerably shorter) instrumental data and extend their results from decades to centuries. In the case of the historical simulation we find that most continental sites have correlation exponents γ between 0.8 and 0.6. For the ocean sites the long-term correlations seem to vanish at the equator and become nonstationary at the Arctic and Antarctic circles. In the control run the long-term correlations are less pronounced. Compared with the historical run, the correlation exponents are increased, and show a more pronounced latitude dependence, visible also at continental sites. When analyzing biannual averages, we find stronger long-term correlations in the historical run at continental sites and a less pronounced latitude dependence. In all cases, the exponent γ does not depend on the continentality of the sites.

On the statistics of urban heat island intensity

[1]xa0We perform a systematic study of all cities in Europe to assess the Urban Heat Island (UHI) intensity by means of remotely sensed land surface temperature data. Defining cities as spatial clusters of urban land cover, we investigate the relationships of the UHI intensity, with the cluster size and the temperature of the surroundings. Our results show that in Europe, the UHI intensity in summer has a strong correlation with the cluster size, which can be well fitted by an empirical sigmoid model. Furthermore, we find a novel seasonality of the UHI intensity for individual clusters in the form of hysteresis-like curves. We characterize the shape and identify apparent regional patterns.

Evidence for long‐term memory in sea level

Detection and attribution of anthropogenic climate change signals in sea level rise (SLR) has experienced considerable attention during the last decades. Here we provide evidence that superimposed on any possible anthropogenic trend there is a significant amount of natural decadal and multidecadal variability. Using a set of 60 centennial tide gauge records and an ocean reanalysis, we find that sea levels exhibit long-term correlations on time scales up to several decades that are independent of any systematic rise. A large fraction of this long-term variability is related to the steric component of sea level, but we also find long-term correlations in current estimates of mass loss from glaciers and ice caps. These findings suggest that (i) recent attempts to detect a significant acceleration in regional SLR might underestimate the impact of natural variability and (ii) any future regional SLR threshold might be exceeded earlier/later than from anthropogenic change alone.

The myth of global science collaboration—Collaboration patterns in epistemic communities

Scientific collaboration is often perceived as a joint global process that involves researchers worldwide, regardless of their place of work and residence. Globalization of science, in this respect, implies that collaboration among scientists takes place along the lines of common topics and irrespective of the spatial distances between the collaborators. The networks of collaborators, termed epistemic communities, should thus have a space-independent structure. This paper shows that such a notion of globalized scientific collaboration is not supported by empirical data. It introduces a novel approach of analyzing distance-dependent probabilities of collaboration. The results of the analysis of six distinct scientific fields reveal that intra-country collaboration is about 10-50 times more likely to occur than international collaboration. Moreover, strong dependencies exist between collaboration activity (measured in co-authorships) and spatial distance when confined to national borders. However, the fact that distance becomes irrelevant once collaboration is taken to the international scale suggests a globalized science system that is strongly influenced by the gravity of local science clusters. The similarity of the probability functions of the six science fields analyzed suggests a universal mode of spatial governance that is independent from the mode of knowledge creation in science.

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.