Multifractal analyses of daily rainfall time series in Pearl River basin of China

The multifractal properties of daily rainfall time series at the stations in Pearl River basin of China over periods of up to 45 years are examined using the universal multifractal approach based on the multiplicative cascade model and the multifractal detrended fluctuation analysis (MF-DFA). The results from these two kinds of multifractal analyses show that the daily rainfall time series in this basin have multifractal behavior in two different time scale ranges. It is found that the empirical multifractal moment function $K(q)$ of the daily rainfall time series can be fitted very well by the universal mulitifractal model (UMM). The estimated values of the conservation parameter $H$ from UMM for these daily rainfall data are close to zero indicating that they correspond to conserved fields. After removing the seasonal trend in the rainfall data, the estimated values of the exponent $h(2)$ from MF-DFA indicate that the daily rainfall time series in Pearl River basin exhibit no long-term correlations. It is also found that $K(2)$ and elevation series are negatively correlated. It shows a relationship between topography and rainfall variability.Comment: 16 pages, 7 figures, 1 table, accepted by Physica

Variability of Persistent Temporal Correlation in Climate Data

This dissertation examines manifestations of persistent memory in climate data. Persistence is characterized by a slow power-law decay in the autocorrelations of a time series. Its existence implies that the influence of past values in a time series extend into the distant future. It has numerous theoretical implications, notably that it changes the asymptotic decay in the variance of sample means, which can substantially impact the uncertainty in climate mean states. Its intensity can vary over space, time, and other dimensions, e.g. tree species. Variation in its intensity can be used for practical applications such as discriminating between steady and intermittent rainfall and assessing the calibration period needed for paleoclimate proxy data. This work explores three major areas in which persistence can be leveraged to better understand the complexities of climate data. The first is in tree ring width data, which are among the best proxies for reconstructing paleoclimate records. The persistent correlations found in tree ring data suggest that the behavior of tree ring growth observed in a short calibration period may be similar to the general behavior of tree ring growth in a much longer period; therefore, the limited calibration period may be more useful than previously thought. The second area is in the quantification of uncertainty in the mean states of climate data. A framework for quantifying uncertainty in climate means is presented which can account for both classical short-range correlations and long-term persistent correlations. The final area is in the detection of subtle changes in tropical rainfall patterns. Persistence is used to illuminate recent changes in the temporal clustering patterns of rainfall in the tropical belt; the detected changes could have critical implications for the water resource management of the affected regions

Simulation of near-term climate change at target sites in West and East Africa

We describe the generation of synthetic sequences of precipitation and maximum and minimum daily temperatures at two locations, in western and eastern Africa respectively. The sequences are generated at the monthly time scale and incorporate both explicitly modelled annual-to-decadal variability, based on the observational record, and long-range (i.e., climate change) trends, as inferred from an ensemble of global climate models. Annual-to-decadal variability is modelled as a first-order vector autoregressive (VAR) process, and the simulations are temporally downscaled to monthly time resolution using a nonparametric resampling scheme. The modelled sequences reproduce well the observed covariances as well as serial autocorrelation in individual variables. The simulations are intended to drive agricultural or other applications models to investigate responses to a range of plausible trends, on which are superimposed decade-scale climate fluctuations whose likelihood of occurrence can be estimated

Long-Term Correlations and Cross-Correlations in Meteorological Variables and Air Pollution in a Coastal Urban Region

In this work, we evaluated the evolution of some atmospheric pollutants (O3, NOx and PM10) over time and their relationship with four different climate variables (solar irradiation, air temperature, relative humidity and wind speed). To this end, we assessed the long-range dependence of those concentrations with a Detrended Fluctuation Analysis (DFA) and analyzed the cross-correlation of such dependence with the climate variables through a Detrended Cross-Correlation Coefficient Analysis (ρDCCA). The results show that air pollution tends to increase over time, impairing air quality and likely affecting human health. The results indicate a cross-correlation between air pollution and the climatic variables, which persisted for a certain period, with a greater correlation between O3 concentration and wind, mainly temperature, and a negative correlation with humidity for all monitoring stations. Moreover, unlike O3 and PM10, NOx concentrations always had a persistent behavior in the region of study for the entire analyzed period.N/

Persistence in complex systems

Persistence is an important characteristic of many complex systems in nature, related to how long the system remains at a certain state before changing to a different one. The study of complex systems' persistence involves different definitions and uses different techniques, depending on whether short-term or long-term persistence is considered. In this paper we discuss the most important definitions, concepts, methods, literature and latest results on persistence in complex systems. Firstly, the most used definitions of persistence in short-term and long-term cases are presented. The most relevant methods to characterize persistence are then discussed in both cases. A complete literature review is also carried out. We also present and discuss some relevant results on persistence, and give empirical evidence of performance in different detailed case studies, for both short-term and long-term persistence. A perspective on the future of persistence concludes the work.This research has been partially supported by the project PID2020-115454GB-C21 of the Spanish Ministry of Science and Innovation (MICINN). This research has also been partially supported by Comunidad de Madrid, PROMINT-CM project (grant ref: P2018/EMT-4366). J. Del Ser would like to thank the Basque Government for its funding support through the EMAITEK and ELKARTEK programs (3KIA project, KK-2020/00049), as well as the consolidated research group MATHMODE (ref. T1294-19). GCV work is supported by the European Research Council (ERC) under the ERC-CoG-2014 SEDAL Consolidator grant (grant agreement 647423)

Persistence in complex systems

Persistence is an important characteristic of many complex systems in nature, related to how long the system remains at a certain state before changing to a different one. The study of complex systems’ persistence involves different definitions and uses different techniques, depending on whether short-term or long-term persistence is considered. In this paper we discuss the most important definitions, concepts, methods, literature and latest results on persistence in complex systems. Firstly, the most used definitions of persistence in short-term and long-term cases are presented. The most relevant methods to characterize persistence are then discussed in both cases. A complete literature review is also carried out. We also present and discuss some relevant results on persistence, and give empirical evidence of performance in different detailed case studies, for both short-term and long-term persistence. A perspective on the future of persistence concludes the work.This research has been partially supported by the project PID2020-115454GB-C21 of the Spanish Ministry of Science and Innovation (MICINN). This research has also been partially supported by Comunidad de Madrid, PROMINT-CM project (grant ref: P2018/EMT-4366). J. Del Ser would like to thank the Basque Government for its funding support through the EMAITEK and ELKARTEK programs (3KIA project, KK-2020/00049), as well as the consolidated research group MATHMODE (ref. T1294-19). GCV work is supported by the European Research Council (ERC) under the ERC-CoG-2014 SEDAL Consolidator grant (grant agreement 647423)

Temporal scaling phenomena in groundwater-floodplain systems using robust detrended fluctuation analysis

In order to determine objectively the fractal behaviour of a time series, and to facilitate potential future attempts to assess model performance by incorporating fractal behaviour, a multi-order robust detrended fluctuation analysis (r-DFAn) procedure is developed herein. The r-DFAn procedure allows for robust and automated quantification of mono-fractal behaviour. The fractal behaviour is quantified with three parts: a global scaling exponent, crossovers, and local scaling exponents. The robustness of the r-DFAn procedure is established by the systematic use of robust regression, piecewise linear regression, Analysis of Covariance (ANCOVA) and Multiple Comparison Procedure to determine statistically significant scaling exponents and optimum crossover locations. The MATLAB code implementing the r-DFAn procedure has also been open sourced to enable reproducible results. r-DFAn will be illustrated on a synthetic signal after which is used to analyse high-resolution hydrologic data; although the r-DFAn procedure is not limited to hydrological or geophysical time series. The hydrological data are 4 year-long datasets (January 2012 to January 2016) of 1-min groundwater level, river stage, groundwater and river temperature, and 15-min precipitation and air temperature, at Wallingford, UK. The datasets are analysed in both time and fractal domains. The study area is a shallow riparian aquifer in hydraulic connection to River Thames, which traverses the site. The unusually high resolution datasets, along with the responsive nature of the aquifer, enable detailed examination of the various data and their interconnections in both time- and fractal-domains

Fluctuation regimes of soil moisture in ERA-40 re-analysis data

Soil moisture variability is analysed in the re-analysis data ERA-40 of the European Centre for Medium-Range Weather Forecasts (ECMWF) which includes four layers within 189 cm depth. Short-term correlations are characterised by an e-folding time scale assuming an exponential decay, whilst long-term memory is described by power law decays with exponents determined by detrended fluctuation analysis. On a global scale, the short-term variability varies congruently with long-term memory in the surface layer. Key climatic regions (Europe, Amazon and Sahara) reveal that soil moisture time series are non-stationary in arid regions and in deep layers within the time horizon of ERA-40. The physical processes leading to soil moisture variability are linear according to an analysis of volatility (the absolute differences), which is substantiated by surrogate data analysis preserving the long-term memory