Timescale Dependence Research Articles

BL LAC OBJECT PKS B1144–379: AN EXTREME SCINTILLATOR

Rapid variability in the radio flux density of the BL Lac object PKSB1144-379 has been observed at four frequencies, ranging from 1.5 to 15 GHz, with the VLA and the University of Tasmania's Ceduna antenna. Intrinsic and line of sight effects were examined as possible causes of this variability, with interstellar scintillation best explaining the frequency dependence of the variability timescales and modulation indices. This scintillation is consistent with a compact source 20-40 microarcseconds, or 0.15-0.3 pc in size. The inferred brightness temperature for PKSB1144-379 (assuming that the observed variations are due to scintillation) is 6.2e12 K at 4.9 GHz, with approximately 10 percent of the total flux in the scintillating component. We show that scintillation surveys aimed at identifying variability timescales of days to weeks are an effective way to identify the AGN with the highest brightness temperatures.

An Investigation of the Short-Term Predictability of Precipitation Using High-Resolution Composite Radar Observations

AbstractThe short-term predictability of precipitation patterns observed by meteorological radar is an important concept as it establishes a means to characterize precipitation and provides an upper limit on the extent of useful nowcasting. Predictability also varies on the basis of spatial and temporal scales of the observed meteorological phenomena. This paper describes an investigation of the short-term predictability of precipitation patterns containing microalpha (0.2–2 km) to mesobeta (20–200 km) scales using high-resolution (0.5 km–1 min–1 dBZ) composite radar reflectivity data, extending the analysis presented in previous work to smaller space and time scales. An experimental approach is used in which continuous and categorical lifetimes of radar reflectivity fields in Eulerian and Lagrangian space are used to quantify short-term predictability. The space–time scale dependency of short-term predictability is analyzed, and a practical upper limit on the extent of Lagrangian persistence-based nowcasting is estimated. Connections to the predictability of larger scales are made within the context of previous work. The results show that short-term predictability estimates in terms of lifetime are approximately 14–15 and 20–21 min in Eulerian and Lagrangian space, respectively, and suggest that a linear relationship exists between predictability and space–time structure from microalpha to macrobeta (2000–10 000 km) scales.

Time-scale dependence in numerical simulations: Assessment of physical, chemical, and biological predictions in a stratified lake at temporal scales of hours to months

We evaluated the predictive ability of a one-dimensional coupled hydrodynamic-biogeochemical model across multiple temporal scales using wavelet analysis and traditional goodness-of-fit metrics. High-frequency in situ automated sensor data and long-term manual observational data from Lake Mendota, Wisconsin, USA, were used to parameterize, calibrate, and evaluate model predictions. We focused specifically on short-term predictions of temperature, dissolved oxygen, and phytoplankton biomass over one season. Traditional goodness-of-fit metrics indicated more accurate prediction of physics than chemical or biological variables in the time domain. This was confirmed by wavelet analysis in both the time and frequency domains. For temperature, predicted and observed global wavelet spectra were closely related, while observed dissolved oxygen and chlorophyll fluorescence spectral characteristics were not reproduced by the model for key time scales, indicating that processes not modeled may be important drivers of the observed signal. Although the magnitude and timing of physical and biological changes were simulated adequately at the seasonal time scale through calibration, time scale-specific dynamics, for example short-term cycles, were difficult to reproduce, and were relatively insensitive to the effects of varying parameters. The use of wavelet analysis is novel to aquatic ecosystem modeling, is complementary to traditional goodness-of-fit metrics, and allows for assessment of variability at specific temporal scales. In this way, the effect of processes operating at distinct temporal scales can be isolated and better understood, both in situ and in silico. Wavelet transforms are particularly well suited for assessment of temporal and spatial heterogeneity when coupled to high-frequency data from automated in situ or remote sensing platforms.

Influences of tides, weather, and discharge on suspended sediment concentration

This paper presents an analysis of long-term monitoring datasets to determine the influences of different external forcing mechanisms on suspended sediment concentration in Suisun Bay, CA, and to evaluate the degree of timescale dependence in the forcing mechanisms. Time- and frequency-domain time series analytic techniques were used on 2-year-long datasets of suspended sediment concentration, river discharge, and weather variables. Surface and bottom SSC are very closely linked in winter, but less so in other seasons. Wintertime subtidal SSC variability is controlled by precipitation and river discharge. During summer months, control shifts to another undefined forcing mechanism. Fortnightly and monthly tides control background and tidally-varying SSC. The relationship between wind and SSC is statistically significant at certain frequencies, but the wind effect comprises a very small proportion of total subtidal variability. When tested individually, 80% of the variance in SSC can be explained by tides, 55% by discharge – rain, and 65% by wind. Collectively, however, wind, river discharge, and tides in combination explained up to 75% of the variance in subtidal SSC, with the other 25% comprising noise and unknown variables. There is a moderate amount of timescale dependence in the forcing mechanisms, but the dominant tidal processes are consistently present over many timescales of observation.

Using a Renormalization Group to Create Ideal Hierarchical Network Architecture with Time Scale Dependency

SUMMARY This paper employs the nature-inspired approach to investigate the ideal architecture of communication networks as large-scale and complex systems. Conventional architectures are hierarchical with respect to the functions of network operations due entirely to implementation concerns and not to any fundamental conceptual benefit. In contrast, the large-scale systems found in nature are hierarchical and demonstrate orderly behavior due to their space/time scale dependencies. In this paper, by examining the fundamental requirements inherent in controlling network operations, we clarify the hierarchical structure of network operations with respect to time scale. We also describe an attempt to build a new network architecture based on the structure. In addition, as an example of the hierarchical structure, we apply the quasi-static approach to describe user-system interaction, and we describe a hierarchy model developed on the renormalization group approach.

Physical Basis for Long-Lived Electronic Coherence in Photosynthetic Light-Harvesting Systems

The physical basis for observed long-lived electronic coherence in photosynthetic light-harvesting systems is identified using an analytically soluble model. Three physical features are found to be responsible for their long coherence lifetimes, (i) the small energy gap between excitonic states, (ii) the small ratio of the energy gap to the coupling between excitonic states, and (iii) the fact that the molecular characteristics place the system in an effective low-temperature regime, even at ambient conditions. Using this approach, we obtain decoherence times for a dimer model with FMO parameters of ∼160 fs at 77 K and ∼80 fs at 277 K. As such, significant oscillations are found to persist for 600 and 300 fs, respectively, in accord with the experiment and with previous computations. Similar good agreement is found for PC645 at room temperature, with oscillations persisting for 400 fs. The analytic expressions obtained provide direct insight into the parameter dependence of the decoherence time scales.

Comparison of nonideal sorption formulations in modeling the transport of phthalate esters through packed soil columns

Sorption of dimethyl phthalate (DMP), diethyl phthalate (DEP) and dipropyl phthalate (DPP) to two soil materials that vary in organic matter content was investigated using miscible displacement experiments under saturated flow conditions. Generated breakthrough curves (BTCs) were inversely simulated using linear, equilibrium sorption (LE), nonlinear, equilibrium sorption (NL), linear, first-order nonequilibrium sorption (LFO), linear, radial diffusion (LRD), and nonlinear, first-order nonequilibrium sorption (NFO) models. The Akaike information criterion was utilized to determine the preferred model. The LE model could not adequately describe phthalate ester (PE) BTCs in higher organic matter soil or for more hydrophobic PEs. The LFO and LRD models adequately described the BTCs but a slight improvement in curve-fitting was gained in some cases when the NFO model was used. However, none of the models could properly describe the desorptive tail of DPP for the high organic matter soil. Transport of DPP through this soil was adequately predicted when degradation or sorption hysteresis was considered. Using the optimized parameter values along with values reported by others it was shown that the organic carbon distribution coefficient ( K oc ) of PEs correlates well with the octanol/water partition coefficient ( K ow ). Also, a strong relationship was found between the first-order sorption rate coefficient normalized to injection pulse size and compound residence time. A similar trend of timescale dependence was found for the rate parameter in the radial diffusion model. Results also revealed that the fraction of instantaneous sorption sites is dependent on K ow and appears to decrease with the increase in the sorption rate parameter.

Timescale dependence of glacial erosion rates: A case study of Marinelli Glacier, Cordillera Darwin, southern Patagonia

[1] Erosion rates have been estimated for a number of glaciated basins around the world, mostly based on modern observations (last few decades) of sediment fluxes to fjords. We use time-constrained sediment volumes delivered by Marinelli Glacier (55°S), an outlet glacier of the Cordillera Darwin ice cap, southern Patagonian Andes, Tierra del Fuego, to determine erosion rates across different timescales. Sediment volumes are derived using a dense grid of high- and low-frequency single channel seismic data and swath bathymetry data along with piston and Kasten cores. Our results show dramatic differences in erosion rates over different timescales. Erosion rates at Marinelli Glacier diminish about 80% (or by factor of ∼5) with each ten-fold increase in the time span over which erosion rates are averaged: 29.3 mm/yr for the last 45 years, 5.3 mm/yr for the last 364 years, and 0.5 mm/yr for the last 12,500 years. These results indicate that modern sediment yields and erosion rates from temperate tidewater glaciers can exceed long-term values over the time of deglaciation after the Last Glacial Maximum (centennial and millennial timescales) by up to 2 orders of magnitude. In view of the low exhumation rates of Cordillera Darwin (∼0.07 mm/yr average for the last 30 Myr), modern erosion rates could be up to 3 orders of magnitude higher than rates over geological time. We conclude that the pattern of erosion rate variation with time reflects the sensitivity of glaciers to climate variability.

A Mechanism for Local Dissipation of Internal Tides Generated at Rough Topography

Abstract Fine- and micro-structure observations indicate that turbulent mixing is enhanced within O(1) km above rough topography. Enhanced mixing is associated with internal wave breaking and, in many regions of the ocean, has been linked to the breaking and dissipation of internal tides. The generation and dissipation of internal tides are explored in this study using a high-resolution two-dimensional nonhydrostatic numerical model, which explicitly resolves the instabilities leading to wave breaking, configured in an idealized domain with a realistic multiscale topography and flow characteristics. The control simulation, chosen to represent the Brazil Basin region, produces a vertical profile of energy dissipation and temporal characteristics of finescale motions that are consistent with observations. Results suggest that a significant fraction of mixing in the bottom O(1) km of the ocean is sustained by the transfer of energy from the large-scale internal tides to smaller-scale internal waves by nonlinear wave–wave interactions. The time scale of the energy transfer to the smaller scales is estimated to be on the order of a few days. A suite of sensitivity experiments is carried out to examine the dependence of the energy transfer time scale and energy dissipation on topographic roughness, tidal amplitude, and Coriolis frequency parameters. Implications for tidal mixing parameterizations are discussed.

The role of primitive relaxation in the dynamics of aqueous mixtures, nano-confined water and hydrated proteins

The relaxation scenario in aqueous systems, such as mixtures of water with hydrophilic solutes, nano-confined water and hydrated biomolecules, has been shown to exhibit general features, in spite of the huge differences in structure, chemical composition and complexity. Dynamics, in all these systems, invariably shows at least two relaxations: (i) a slower process, related to cooperative and structural motions of water and solute molecules (in the case of mixtures) or related to interfacial processes in the case of confined water and (ii) a faster process, with non-cooperative character originating from water. The latter has properties including timescale and temperature dependence similar or related in all the aqueous systems. This water-specific relaxation can be identified as the primitive relaxation, or the Johari–Goldstein β-relaxation. The primitive process is the precursor of the many-body relaxation process which increases in length-scale with time until the terminal α-relaxation is reached. Using new experimental data (at atmospheric and high pressure) along with a revision of most of the recent literature on the dynamics of confined water and aqueous mixtures, we show that the two abovementioned relaxation processes are inter-related as evidenced by correlations in their properties. For instance, both relaxation time and dielectric strength of the water-specific relaxation exhibit a crossover from a stronger to a weaker dependence with decreasing T, at the temperature where the slow process attains a very long timescale (> 1 ks) and becomes structurally arrested, exactly analogous to that found for β-relaxation in van der Waals liquids. Moreover, the primitive relaxation of water is shown to play a pivotal role in determining the dynamics of hydrated biomolecules in general, including the “dynamic transition” observed by neutron scattering and Mössbauer spectroscopy. We show that the primitive relaxation of the solvent is responsible for the dynamic transition, even in the case that the solvent is not pure water or an aqueous mixture.

Thermal effects on the magnetization reversal process and its interpretation in perpendicular magnetic recording media

We have studied the time-scale and temperature dependence of the magnetization reversal in perpendicular magnetic recording media. One of the under-reported phenomena associated with this reversal is the thermal dependence of the squareness of the magnetic hysteresis loop. Understanding this phenomenon is important because the coercive squareness parameter S∗ is often used to evaluate the strength of the magnetic exchange-coupling interactions between the grains. In this work, we demonstrate that S∗ is a dynamic quantity which depends on the thermal agitation of the magnetization, and it is imperative to take this dependence into account in interpreting magnetic and microstructural effects. Based on the Sharrock model for the dynamic coercivity, we built an expression for the time-scale and temperature dependence of S∗ in highly oriented perpendicular magnetic recording media. Fits of experimental data to the resulting expression were then used to extract the intrinsic squareness parameter Sint∗ which originates in the thermal-independent demagnetization and exchange-interaction effects. Sint∗ was estimated for two sets of perpendicular recording media samples. For the first set of media samples showing progressively smaller grain sizes, the values of S∗ measured at the normal magnetometry time-scales of milliseconds to seconds indicated progressively smaller values. In contrast, the values of the thermal-independent Sint∗ determined from applying the above model were progressively larger. This discrepancy can only be explained on the basis of progressively stronger intergranular exchange coupling, which is offset by strong thermal effects at small grain sizes. For the second set of media samples with increasingly larger segregant oxide content, progressively smaller values of both S∗ and thermal-independent Sint∗ were observed, thus verifying the strong intergranular segregation effects due to greater nonmagnetic grain boundary phase. The phenomenological model for thermal-independent Sint∗ will be helpful in interpreting the microstructural and magnetic properties of perpendicular magnetic recording media, especially as thermal effects become important in the approach to areal densities of 1 Tbits/in2.

Radar rainfall estimation in the context of post-event analysis of flash-flood events

summary A method to estimate rainfall from radar data for post-event analysis of flash-flood events has been developed within the EC-funded HYDRATE project. It follows a pragmatic approach including careful analysis of the observation conditions for the radar system(s) available for the considered case. Clutter and beam blockage are characterised by dry-weather observations and simulations based on a digital terrain model of the region of interest. The vertical profile of reflectivity (VPR) is either inferred from radar data if volume scanning data are available or simply defined using basic meteorological parameters (idealised VPR). Such information is then used to produce correction factor maps for each elevation angle to correct for range-dependent errors. In a second step, an effective Z–R relationship is optimised to remove the bias over the hit region. Due to limited data availability, the optimisation is carried out with reference to raingauge rain amounts measured at the event time scale. Sensitivity tests performed with two welldocumented rain events show that a number of Z = aR b relationships, organised along hyperbolic curves in the (a and b) parameter space, lead to optimum assessment results in terms of the Nash coefficient between the radar and raingauge estimates. A refined analysis of these equifinality patterns shows that the ‘‘total additive conditional bias” can be used to discriminate between the Nash coefficient equifinal solutions. We observe that the optimisation results are sensitive to the VPR description and also that the Z–R optimisation procedure can largely compensate for range-dependent errors, although this shifts the optimal coefficients in the parameter space. The time-scale dependency of the equifinality patterns is significant, however near-optimal Z–R relationships can be obtained at all time scales from the event time step optimisation. 2010 Published by Elsevier B.V.

Temperature dependence of effective fluctuation time scales in spin glasses

Using a series of fast cooling protocols we have probed aging effects in the spin glass state as a function of temperature. Analyzing the logarithmic decay found at very long time scales within a simple phenomenological barrier model, leads to the extraction of the fluctuation time scale of the system at a particular temperature. This is the smallest dynamical time-scale, defining a lower-cut off in a hierarchical description of the dynamics. We find that this fluctuation time scale, which is approximately equal to atomic spin fluctuation time scales near the transition temperature, follows ageneralized Arrhenius law. We discuss the hypothesisthat, upon cooling to a measuring temperature within the spin glass state, there is a range of dynamically in-equivalent configurations in which the system can be trapped, and check within a numerical barrier model simulation, that this leads to sub-aging behavior in scaling aged TRM decay curves, as recently discussed theoretically, see arXiv:0902.3556 .

Comparison of daubechies wavelets for hurst parameter estimation

Time scale dependence on the working nature of wavelet analysis makes it a valuable tool for Hurst parameter estimation. Similar to other wavelet-based signal processing applications, the selection of a particular wavelet type and vanishing moment in wavelet based Hurst estimation is a challenging problem. In this paper, we investigate the best Daubechies wavelet in wavelet based Hurst estimation for an exact self similar process, fractional Gaussian noise and how Daubechies vanishing moment affects the Hurst estimation accuracy. Daubechies wavelets are preferred in analysis because increasing vanishing moment does not cause excessive increase of time support of Daubechies wavelets. Thus, limited time support of wavelets reduces the border effects. Results show that Daubechies wavelets with one vanishing moment (Daubechies 1) gives the best estimation result for short range dependent fractional Gaussian noise. Daubechies 2 is the best preference for long range dependent fractional Gaussian noise.

Time - the emerging dimension of plant virus studies

Recent research has revealed that some plant viruses, like many animal viruses, have measurably evolving populations. Most of these viruses have single-stranded positive-sense RNA genomes, but a few have single-stranded DNA genomes. The studies show that extant populations of these viral species are only decades to centuries old. The genera in which they are placed have diverged since agriculture was invented and spread around the world during the Holocene period. We suggest that this is not mere coincidence but evidence that the conditions generated by agriculture during this era have favoured particular viruses. There is also evidence, albeit less certain, that some plant viruses, including a few shown to have measurably evolving populations, have much more ancient origins. We discuss the possible reasons for this clear discordance between short- and long-term evolutionary rate estimates and how it might result from a large timescale dependence of the evolutionary rates. We also discuss briefly why it is useful to know the rates of evolution of plant viruses.

Time scale and intensity dependency in multiplicative cascades for temporal rainfall disaggregation

Multiplicative random cascades (MRCs) can parsimoniously generate highly intermittent patterns similar to those in rainfall. The elemental MRC model parameter is the cascade weight, which determines how rainfall at one scale is partitioned at the next smallest scale in the cascade. While it is known that the probability density of these weights may vary with both time scale and rainfall intensity, nearly all previous studies have considered either time scale or intensity separately. We examined the simultaneous dependency of the weights on both factors and assessed the impacts of explicitly including these dependencies in the MRC model. On the basis of the observed relationships between cascade weights and time scale and intensity, four progressively more “dependent” models were constructed to disaggregate a long time series of daily rainfall to hourly intervals. We found that inclusion of the intensity dependency on the model parameters that generate dry intervals greatly improved performance. For the relatively small range of time scales over which the rainfall was disaggregated, varying model parameters with time scale resulted in minor improvement.

CROSS-FIELD DIFFUSION OF COSMIC RAYS IN TWO-DIMENSIONAL MAGNETIC FIELD TURBULENCE MODELS

We discuss cross-field diffusion of energetic particles using compressional and noncompressional two-dimensional turbulence models by performing test particle simulations. For both models, the diffusion coefficient, defined in the classical way, exhibits a timescale dependence, suggesting that the underlining physical process should be described by Levy statistics. The diffusion coefficient for long timescales is classified in terms of the Kubo number, K = bL ⊥/ρ, where b is the standard deviation of magnetic field fluctuation in units of the background field, ρ is the particle Larmor raduis, and L ⊥ is the field turbulence scale length. While the well-known JKG theorem predicts that a particle cannot move more than about one gyroradius normal to the magnetic field in a system with two or less spatial dimensions, the cross-field diffusion does take place in our models since they are exceptions to the theorem: we argue that particle motion on the flux surface is not prohibited in general, and in particular, it is not bounded when the background magnetic field is exactly parallel to the ignorable coordinate.

Aspect-ratio dependence of transient Taylor vortices close to threshold

We perform a detailed numerical study of transient Taylor vortices arising from the instability of cylindrical Couette flow with the exterior cylinder at rest for radius ratio η = 0.5 and variable aspect ratio Γ. The result of Abshagen et al. (J Fluid Mech 476:335-343, 2003) that onset transients apparently evolve on a much smaller time-scale than decay transients is recovered. It is shown to be an artefact of time scale estimations based on the Stuart-Landau amplitude equation which assumes frozen space dependence while full space-time dependence embedded in the Ginzburg-Landau formalism needs to be taken into account to understand transients already at moderate aspect ratio. Sub-critical pattern induction is shown to explain the apparently anomalous behaviour of the system at onset while decay follows the Stuart-Landau prediction more closely. The dependence of time scales on boundary effects is studied for a wide range of aspect ratios, including non-integer ones, showing general agreement with the Ginzburg-Landau picture able to account for solutions modulated by Ekman pumping at the disks bounding the cylinders.

Signal duration and the time scale dependence of signal integration in biochemical pathways

BackgroundSignal duration (e.g. the time over which an active signaling intermediate persists) is a key regulator of biological decisions in myriad contexts such as cell growth, proliferation, and developmental lineage commitments. Accompanying differences in signal duration are numerous downstream biological processes that require multiple steps of biochemical regulation.ResultsHere we present an analysis that investigates how simple biochemical motifs that involve multiple stages of regulation can be constructed to differentially process signals that persist at different time scales. We compute the dynamic, frequency dependent gain within these networks and resulting power spectra to better understand how biochemical networks can integrate signals at different time scales. We identify topological features of these networks that allow for different frequency dependent signal processing properties.ConclusionWe show that multi-staged cascades are effective in integrating signals of long duration whereas multi-staged cascades that operate in the presence of negative feedback are effective in integrating signals of short duration. Our studies suggest principles for why signal duration in connection with multiple steps of downstream regulation is a ubiquitous motif in biochemical systems.

Fourier-resolved energy spectra of the Narrow-Line Seyfert 1 Mkn 766

We compute Fourier-resolved X-ray spectra of the Seyfert 1 Markarian 766 to study the shape of the variable components contributing to the 0.3-10 keV energy spectrum and their time-scale dependence. The fractional variability spectra peak at 1-3 keV, as in other Seyfert 1 galaxies, consistent with either a constant contribution from a soft excess component below 1 keV and Compton reflection component above 2 keV or variable warm absorption enhancing the variability in the 1-3 keV range. The rms spectra, which show the shape of the variable components only, are well described by a single power law with an absorption feature around 0.7 keV, which gives it an apparent soft excess. This spectral shape can be produced by a power law varying in normalization, affected by an approximately constant (within each orbit) warm absorber, with parameters similar to those found by Turner et al. for the warm-absorber layer covering all spectral components in their scattering scenario [N H ∼ 3 × 10 21 cm -2 , log(ξ) ∼ 1]. The total soft excess in the average spectrum can therefore be produced by a combination of constant warm absorption on the power-law plus an additional less variable component. On shorter time-scales, the rms spectrum hardens and this evolution is well described by a change in power-law slope, while the absorption parameters remain the same. The frequency dependence of the rms spectra can be interpreted as variability arising from propagating fluctuations through an extended emitting region, whose emitted spectrum is a power law that hardens towards the centre. This scenario reduces the short time-scale variability of lower energy bands making the variable spectrum harder on shorter time-scales and at the same time explains the hard lags found in these data by Markowitz et al.