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Register a new userMultifractality of river runoff and precipitation: Comparison of fluctuation analysis and wavelet methods
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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 months, 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.
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We study temporal correlations and multifractal properties of long river discharge records from 41 hydrological stations around the globe. To detect long-term correlations and multifractal behaviour in the presence of trends, we apply several recently developed methods [detrended fluctuation analysis (DFA), wavelet analysis, and multifractal DFA] that can systematically detect and overcome nonstationarities in the data at all time scales. We find that above some crossover time that usually is several weeks, the daily runoffs are long-term correlated, being characterized by a correlation function C(s) that decays as C(s) ~ s^(gamma). The exponent gamma varies from river to river in a wide range between 0.1 and 0.9. The power-law decay of C(s) corresponds to a power-law increase of the related fluctuation function F_2(s) ~ s^H where H = 1-gamma/2. We also find that in most records, for large times, weak multifractality occurs. The Renyi exponent tau(q) for q between -10 and +10 can be fitted to the remarkably simple form tau(q) = -ln(a^q+b^q) /ln 2, with solely two parameters a and b between 0 and 1 with a+b >= 1. This type of multifractality is obtained from a generalization of the multiplicative cascade model.
The Saigon River, which flows through the center of Ho Chi Minh City, is of critical importance for the development of the city as forms as the main water supply and drainage channel for the city. In recent years, riverbank erosion and failures have become more frequent along the Saigon River, causing flooding and damage to infrastructures near the river. A field investigation and numerical study has been undertaken by our research group to identify factors affecting the riverbank failure. In this paper, field investigation results obtained from multiple investigation points on the Saigon River are presented, followed by a comprehensive coupled finite element analysis of riverbank stability when subjected to river water level fluctuations. The river water level fluctuation has been identified as one of the main factors affecting the riverbank failure, i.e. removal of the balancing hydraulic forces acting on the riverbank during water drawdown.
Providing efficient and accurate parametrizations for model reduction is a key goal in many areas of science and technology. Here we present a strong link between data-driven and theoretical approaches to achieving this goal. Formal perturbation expansions of the Koopman operator allow us to derive general stochastic parametrizations of weakly coupled dynamical systems. Such parametrizations yield a set of stochastic integro-differential equations with explicit noise and memory kernel formulas to describe the effects of unresolved variables. We show that the perturbation expansions involved need not be truncated when the coupling is additive. The unwieldy integro-differential equations can be recast as a simpler multilevel Markovian model, and we establish an intuitive connection with a generalized Langevin equation. This connection helps setting up a parallelism between the top-down, equations-based methodology herein and the well-established empirical model reduction (EMR) methodology that has been shown to provide efficient dynamical closures to partially observed systems. Hence, our findings support, on the one hand, the physical basis and robustness of the EMR methodology and, on the other hand, illustrate the practical relevance of the perturbative expansion used for deriving the parametrizations.
Fluctuation geometry was recently proposed as a counterpart approach of Riemannian geometry of inference theory. This theory describes the geometric features of the statistical manifold $mathcal{M}$ of random events that are described by a family of continuous distributions $dp(x|theta)$. A main goal of this work is to clarify the statistical relevance of Levi-Civita curvature tensor $R_{ijkl}(x|theta)$ of the statistical manifold $mathcal{M}$. For this purpose, the notion of emph{irreducible statistical correlations} is introduced. Specifically, a distribution $dp(x|theta)$ exhibits irreducible statistical correlations if every distribution $dp(check{x}|theta)$ obtained from $dp(x|theta)$ by considering a coordinate change $check{x}=phi(x)$ cannot be factorized into independent distributions as $dp(check{x}|theta)=prod_{i}dp^{(i)}(check{x}^{i}|theta)$. It is shown that the curvature tensor $R_{ijkl}(x|theta)$ arises as a direct indicator about the existence of irreducible statistical correlations. Moreover, the curvature scalar $R(x|theta)$ allows to introduce a criterium for the applicability of the emph{gaussian approximation} of a given distribution function. This type of asymptotic result is obtained in the framework of the second-order geometric expansion of the distributions family $dp(x|theta)$, which appears as a counterpart development of the high-order asymptotic theory of statistical estimation. In physics, fluctuation geometry represents the mathematical apparatus of a Riemannian extension for Einsteins fluctuation theory of statistical mechanics. Some exact results of fluctuation geometry are now employed to derive the emph{invariant fluctuation theorems}.
We use detrended fluctuation analysis (DFA) to study the dynamics of blood pressure oscillations and its feedback control in rats by analyzing systolic pressure time series before and after a surgical procedure that interrupts its control loop. We found, for each situation, a crossover between two scaling regions characterized by exponents that reflect the nature of the feedback control and its range of operation. In addition, we found evidences of adaptation in the dynamics of blood pressure regulation a few days after surgical disruption of its main feedback circuit. Based on the paradigm of antagonistic, bipartite (vagal and sympathetic) action of the central nerve system, we propose a simple model for pressure homeostasis as the balance between two nonlinear opposing forces, successfully reproducing the crossover observed in the DFA of actual pressure signals.
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