Stochastic similarities between the microscale of turbulence and hydro-meteorological processes

ABSTRACT

Turbulence is considered to generate and drive most geophysical processes. The simplest case is isotropic turbulence. In this paper, the most common three-dimensional power-spectrum-based models of isotropic turbulence are studied in terms of their stochastic properties. Such models often have a high order of complexity, lack stochastic interpretation and violate basic stochastic asymptotic properties, such as the theoretical limits of the Hurst coefficient, when Hurst-Kolmogorov behaviour is observed. A simpler and robust model (which incorporates self-similarity structures, e.g. fractal dimension and Hurst coefficient) is proposed using a climacogram-based stochastic framework and tested over high-resolution observational data of laboratory scale as well as hydro-meteorological observations of wind speed and precipitation intensities. Expressions of other stochastic tools such as the autocovariance and power spectrum are also produced from the model and show agreement with data. Finally, uncertainty, discretization and bias related errors are estimated for each stochastic tool, showing lower errors for the climacogram-based ones and larger for power spectrum ones.     

Predictability in dice motion: how does it differ from hydro-meteorological processes?

ABSTRACT

From ancient times dice have been used to denote randomness. A dice throw experiment is set up in order to examine the predictability of the die orientation through time using visualization techniques. We apply and compare a deterministic-chaotic model and a stochastic model and we show that both suggest predictability in die motion that deteriorates with time, just as in hydro-meteorological processes. Namely, a die’s trajectory can be predictable for short horizons and unpredictable for long ones. Furthermore, we show that the same models can be applied, with satisfactory results, to high temporal resolution time series of rainfall intensity and wind speed magnitude, occurring during mild and strong weather conditions. The difference among the experimental and two natural processes is in the time length of the high-predictability window, which is of the order of 0.1 s, 10 min and 1 h for dice, rainfall and wind processes, respectively.     

Climacogram versus autocovariance and power spectrum in stochastic modelling for Markovian and Hurst–Kolmogorov processes

Three common stochastic tools, the climacogram i.e. variance of the time averaged process over averaging time scale, the autocovariance function and the power spectrum are compared to each other to assess each one’s advantages and disadvantages in stochastic modelling and statistical inference. Although in theory, all three are equivalent to each other (transformations one another expressing second order stochastic properties), in practical application their ability to characterize a geophysical process and their utility as statistical estimators may vary. In the analysis both Markovian and non Markovian stochastic processes, which have exponential and power-type autocovariances, respectively, are used. It is shown that, due to high bias in autocovariance estimation, as well as effects of process discretization and finite sample size, the power spectrum is also prone to bias and discretization errors as well as high uncertainty, which may misrepresent the process behaviour (e.g. Hurst phenomenon) if not taken into account. Moreover, it is shown that the classical climacogram estimator has small error as well as an expected value always positive, well-behaved and close to its mode (most probable value), all of which are important advantages in stochastic model building. In contrast, the power spectrum and the autocovariance do not have some of these properties. Therefore, when building a stochastic model, it seems beneficial to start from the climacogram, rather than the power spectrum or the autocovariance. The results are illustrated by a real world application based on the analysis of a long time series of high-frequency turbulent flow measurements.     

Nonlinear dynamic analysis of multi-base seismically isolated structures with uplift potential II： verification examples

The work presented in this paper serves as numerical verification of the analytical model developed in the companion paper for nonlinear dynamic analysis of multi-base seismically isolated structures. To this end, two numerical examples have been analyzed using the computational algorithm incorporated into program 3D-BASIS-ME-MB, developed on the basis of the newly-formulated analytical model. The first example concerns a seven-story model structure that was tested on the earthquake simulator at the University at Buffalo and was also used as a verification example for program SAP2000. The second example concerns a two-tower, multi-story structure with a split-level seismic-isolation system. For purposes of verification, key results produced by 3D-BASIS-ME-MB are compared to experimental results, or results obtained from other structural/finite element programs. In both examples, the analyzed structure is excited under conditions of bearing uplift, thus yielding a case of much interest in verifying the capabilities of the developed analysis tool.     

Spatial seismic modeling of base‐isolated buildings pounding against moat walls: effects of ground motion directionality and mass eccentricity

Structural impact between adjacent buildings may induce local and, in some extreme cases, severe damage, especially in the case of seismically isolated buildings. This study parametrically investigates in the three‐dimensional domain the effect of pounding on the peak response of base‐isolated buildings, which are simulated as nonlinear three‐dimensional multi‐degree‐of‐freedom systems. Firstly, it is shown that considering unidirectional, instead of bidirectional, excitations may lead to underestimation of the base drift demands. Subsequently, the peak responses of seismically isolated buildings utilizing lead rubber bearings are studied while varying important parameters, such as the incidence angle of seismic excitations, the available seismic clearance, and mass eccentricities, under the action of bidirectional horizontal excitations. A large number of numerical simulations are performed using a specially developed software that implements an efficient approach to model impacts, taking into account arbitrary locations of contact points. It is found that the peak interstory drift ratio is significantly influenced by the directionality of the ground motion. Therefore, the seismic performance of structures should ideally be assessed examining the peak structural response while bidirectional ground motions are imposed at various incident angles. Furthermore, it is also observed that the interstory drift ratios increase while decreasing the available gap size, up to a certain value. Finally, the parametric analyses indicate that the effects of impact are more severe for structures with mass eccentricities, and in which case, the estimation of the critical incidence angle becomes more laborious. Copyright © 2016 John Wiley & Sons, Ltd.     

Engineering geological characterization of low strength anisotropic rocks in the Himalayan region for assessment of tunnel support

A detailed engineering geological assessment of low strength (6–35 MPa) anisotropic rocks at an ongoing Hydroelectric Project in the Himalayan Region has been carried out. The project (the Nathpa Jhakri Hydroelectric Project) will have one of the world's largest and longest water conducting systems, consisting of a 10.15 m diameter and 27.3 km long head race tunnel, a 942 000 m³ underground desilting complex and a 20 × 49 × 216 m powerhouse cavern in the area. Because these constructions are made in low strength metamorphosed anisotropic rocks like quartz mica schists, biotite schists and muscovite schists, it seemed necessary and worthwhile to undertake a comprehensive study of such rocks. The studies include petrographic and petrofabric analyses of the rocks, geo-mechanical properties, rock stress measurements, rock mass classification using the Q-System and data concerning joint geometry, joint roughness and joint strength. The use of mapped geological and geotechnical data along with the experimental and modelling studies have helped to better understand the behaviour of these rocks in underground openings.     

Differential bedload transport rates in a gravel-bed stream: A grain-size distribution approach

Two methods that were recently proposed for calculating fractional bedload transport rates in gravel-bed streams are examined closely. Both of them employ the Oak Creek bedload data. The Diplas (PD) method is guided by dimensional analysis and, therefore, can be used to predict bedload transport in different gravel rivers. The only requirement for using this method is the knowledge of the subsurface material size distribution of the stream of interest. The expression for the fractional bedload transport obtained by the Shih and Komar (SK) method for Oak Creek cannot be used for other streams. Its use for a given stream requires information that is rarely available. For the Oak Creek case both methods demonstrate similar predictive ability.     

Prediction of coarse particle movement with adaptive neuro‐fuzzy inference systems

The use of a neuro‐fuzzy approach is proposed to model the dynamics of entrainment of a coarse particle by rolling. It is hypothesized that near‐bed turbulent flow structures of different magnitude and duration or frequency and energy content are responsible for the particle displacement. A number of Adaptive Neuro‐Fuzzy Inference System (ANFIS) architectures are proposed and developed to link the hydrodynamic forcing exerted on a solid particle to its response, and model the underlying nonlinear dynamics of the system. ANFIS combines the advantages of fuzzy inference (If‐Then) rules with the power of learning and adaptation of the neural networks. The model components and forecasting procedure are discussed in detail. To demonstrate the model's applicability for near‐threshold flow conditions an example is provided, where flow velocity and particle displacement data from flume experiments are used as input and output for the training and testing of the ANFIS models. In particular, a Laser Doppler velocimeter (LDV) is employed to obtain long records of local streamwise velocity components upstream of a mobile exposed particle. These measurements are acquired synchronously with the time history of the particle's position detected by a setup including a He‐Ne laser and a photodetector. The representation of the input signal in the time and frequency domain is implemented and the best performing models are found capable of reproducing the complex dynamics of particle response. Following a trial and error approach the different models are compared in terms of their efficiency and forecast accuracy using a number of performance indices. Copyright © 2011 John Wiley & Sons, Ltd.     

Identifying the occurrence time of an impending major earthquake: a review

The procedure through which the occurrence time of an impending major earthquake can be determined is reviewed in the light of the recent advances. This can be achieved by analyzing in natural time the seismicity in the candidate area. To apply this general procedure, we need two important elements: first, to know when we should start the analysis, i.e., set the natural time equal to zero. This is the time at which the system enters the critical stage. Second a reliable estimation of the candidate epicentral area. If geoelectrical measurements are taken and the VAN method (after the initials of the three researchers Varotsos, Alexopoulos and Nomicos) is applied, both these elements become available upon the recording of a precursory Seismic Electric Signals (SES) activity, because its initiation marks the time when the system enters the critical stage, and in addition the SES data enable the determination of the epicentral area of the impending mainshock. On the other hand, if geoelectrical data are lacking, we make use of the following two recent findings by means of natural time analysis: First, the fluctuations of the order parameter of seismicity in a large area exhibit a minimum a few months before a major earthquake almost simultaneously with the initiation of an SES activity. Second, a spatiotemporal study of this minimum unveils an estimate of the epicentral area of the impending major earthquake. Two examples are given that refer to the strongest earthquakes that occurred in Greece and Japan during the last 3 decades, i.e., the M _W6.9 earthquake in southwestern Greece on 14 February 2008 and the M _W9.0 Tohoku earthquake in Japan on 11 March 2011.