Scaling Breaks Research Articles

Turbulent Airflow and Wave-Induced Stress Over the Ocean

We examine the structure of turbulent airflow over ocean waves. Based on an analysis of wind and wave observations derived from a moored and floating Air–Sea Interaction Spar buoy during the Shoaling Waves Experiment field campaign, we show that the cospectra of momentum flux for wind–sea conditions follow established universal scaling laws. Under swell-dominant conditions, the wave boundary layer is extended and the universal cospectral scaling breaks down, as demonstrated previously. On the other hand, the use of peak wave frequency to reproduce the universal cospectra successfully explains the structure of the turbulent flow field. We quantify the wave-coherent component of the airflow and this clarifies how ocean waves affect momentum transfer through the wave boundary layer. In fact, the estimated wave-induced stresses for swell-dominant conditions explain the anomalous cospectral shapes observed near the peak wave frequency.

Understanding the scaling of electron kinetics in the transition from collisional to collisionless conditions in microscale gas discharges

When gas discharge and plasma devices shrink to the microscale, the electrode distance in the device approaches the mean free path of electrons and they experience few collisions. As microscale gas discharge and plasma devices become more prevalent, the behavior of discharges at these collisionless and near-collisionless conditions need to be understood. In conditions where the characteristic length d is much greater than the mean free path λ (i.e., macroscopic conditions), electron energy distributions (EEDs) and rate coefficients scale with the reduced electric field E/p. However, when d is comparable with or much lower than λ, this E/p scaling breaks. In this work, particle-in-cell/Monte Carlo collision simulations are used to explore the behavior of the EED and subsequent reaction rate coefficients in microscale field emission-driven Townsend discharges for both an atomic (argon) and a molecular (hydrogen) gas. To understand the behavior, a pseudo-analytical model is developed for the spatially integrated EED and rate coefficients in the collisional to collisionless transition regime based on the weighted sum of a fully collisional, two-temperature Maxwellian EED and the ballistic EED. The theory helps clarify the relative contribution of ballistic electrons in these extreme conditions and can be used to more accurately predict when macroscopic E/p scaling fails at the microscale.

Scaling Analysis of Temperature and Liquid Water Content in the Marine Boundary Layer Clouds during POST

AbstractThe authors have analyzed the scaling behavior of marine boundary layer (MBL) clouds using high-resolution temperature (T) and liquid water content (LWC) fluctuations from aircraft measurements collected over the Pacific Ocean during the Physics of Stratocumulus Top (POST) research campaign in summer of 2008. As an extension of the past studies for scale-invariant properties of MBL clouds, the authors studied the variability of scaling exponents with height. The results showed that both LWC and T have two distinct scaling regimes: the first one displays scale invariance over a range from about 1–5 m to at least 7 km, and the second one goes from about 0.1–1 to 1–5 m. For the large-scale regime (r > 1–5 m), turbulence in MBL clouds is multifractal, while scale break and scaling exponents vary with height, most significantly in the cloud-top region. For example, LWC spectral exponent β increases from 1.42 at cloud base to 1.58 at cloud top, while scale break decreases from ~5 m at cloud base to 0.8 m at cloud top. The bifractal parameters (H1, C1) for LWC increase from (0.14, 0.02) at cloud base to (0.33, 0.1) at cloud top while maintaining a statistically significant linear relationship C1 ≈ 0.4H1 − 0.04 in MBL clouds. From near surface to cloud top, (H1, C1) for T also increase with height, but above cloud top H1 increases and C1 decreases with height. The results suggest the existence of three turbulence regimes: near the surface, in the middle of the boundary layer, and in the cloud-top region, which need to be distinguished.

Multifractal evaluation of simulated precipitation intensities from the COSMO NWP model

Abstract. The framework of universal multifractals (UM) characterizes the spatio-temporal variability in geophysical data over a wide range of scales with only a limited number of scale-invariant parameters. This work aims to clarify the link between multifractals (MFs) and more conventional weather descriptors and to show how they can be used to perform a multi-scale evaluation of model data. The first part of this work focuses on a MF analysis of the climatology of precipitation intensities simulated by the COSMO numerical weather prediction model. Analysis of the spatial structure of the MF parameters, and their correlations with external meteorological and topographical descriptors, reveals that simulated precipitation tends to be smoother at higher altitudes, and that the mean intermittency is mostly influenced by the latitude. A hierarchical clustering was performed on the external descriptors, yielding three different clusters, which correspond roughly to Alpine/continental, Mediterranean and temperate regions. Distributions of MF parameters within these three clusters are shown to be statistically significantly different, indicating that the MF signature of rain is indeed geographically dependent. The second part of this work is event-based and focuses on the smaller scales. The MF parameters of precipitation intensities at the ground are compared with those obtained from the Swiss radar composite during three events corresponding to typical synoptic conditions over Switzerland. The results of this analysis show that the COSMO simulations exhibit spatial scaling breaks that are not present in the radar data, indicating that the model is not able to simulate the observed variability at all scales. A comparison of the operational one-moment microphysical parameterization scheme of COSMO with a more advanced two-moment scheme reveals that, while no scheme systematically outperforms the other, the two-moment scheme tends to produce larger extreme values and more discontinuous precipitation fields, which agree better with the radar composite.

Four-Loop Nonplanar Cusp Anomalous Dimension in N=4 Supersymmetric Yang-Mills Theory.

The lightlike cusp anomalous dimension is a universal function that controls infrared divergences in quite general gauge theories. In the maximally supersymmetric Yang-Mills theory this function is fixed fully by integrability to the three-loop order. At four loops a nonplanar correction appears which we obtain for the first time from a numerical computation of the Sudakov form factor. Key ingredients are widely applicable methods to control the number-theoretic aspects of the appearing integrals. Our result shows explicitly that quadratic Casimir scaling breaks down at four loops.

Seafloor Geomorphology and Processes on the Western Continental Margin of India based on Multibeam Acoustic Backscatter Data Analysis

ABSTRACTAn assessment of the multibeam sonar data of the central Western Continental Margins of India has been carried out to evaluate the seafloor geomorphology and processes by examining the geomorphological attributes e.g., slope, sediments, structures, etc. associated with geomorphic features. The variation in relief and the features located in the region have been mapped and interpreted collectively by utilizing several geospatial mapping tools. The backscatter strength across the area, apparently congruent with the local relief, has helped to examine the sediment movement on the seafloor. The prominent features found in the region include faults, pockmarks, mounds, submarine terraces, and submerged fossil reefs. Several areas with varying topography engender comparable fractal dimension at short scale breaks, and the probability density functions (PDFs) utilizing backscatter data depicting overlapping classes. The present study highlights how fractals and scale break parameters can be utilized to determine the seafloor processes and associated sedimentological dynamics in a complex geographical environment with strong bottom currents, seasonal upwelling, and faulted structure. The role and impact of the various geomorphic processes on the reworking of sediment movement and the overall progression of the seafloor morphology has been revealed for the first time in this part of the ocean bottom.

Multiresolution analysis of characteristic length scales with high‐resolution topographic data

AbstractCharacteristic length scales (CLS) define landscape structure and delimit geomorphic processes. Here we use multiresolution analysis (MRA) to estimate such scales from high‐resolution topographic data. MRA employs progressive terrain defocusing, via convolution of the terrain data with Gaussian kernels of increasing standard deviation, and calculation at each smoothing resolution of (i) the probability distributions of curvature and topographic index (defined as the ratio of slope to area in log scale) and (ii) characteristic spatial patterns of divergent and convergent topography identified by analyzing the curvature of the terrain. The MRA is first explored using synthetic 1‐D and 2‐D signals whose CLS are known. It is then validated against a set of MARSSIM (a landscape evolution model) steady state landscapes whose CLS were tuned by varying hillslope diffusivity and simulated noise amplitude. The known CLS match the scales at which the distributions of topographic index and curvature show scaling breaks, indicating that the MRA can identify CLS in landscapes based on the scaling behavior of topographic attributes. Finally, the MRA is deployed to measure the CLS of five natural landscapes using meter resolution digital terrain model data. CLS are inferred from the scaling breaks of the topographic index and curvature distributions and equated with (i) small‐scale roughness features and (ii) the hillslope length scale.

Scaling characteristics of mountainous river flow fluctuations determined using a shallow-water acoustic tomography system

The aim of this study is to investigate the scaling exponent properties of mountainous river flow fluctuations by detrended fluctuation analysis (DFA). Streamflow data were collected continuously using Fluvial Acoustic Tomography System (FATS), which is a novel system for measuring continuous streamflow at high-frequency scales. The results revealed that river discharge fluctuations have two scaling regimes and scaling break. In contrast to the Ranting Curve method (RC), the small-scale exponent detected by the FATS is estimated to be 1.02 ± 0.42% less than that estimated by RC. More importantly, the crossover times evaluated from the FATS delayed approximately by 42 ± 21 hr ≈2–3 days than their counterparts estimated by RC. The power spectral density analysis assists our findings. We found that scaling characteristics information evaluated for a river using flux data obtained by RC approach might not be accurately detected, because this classical method assumes that flow in river is steady and depends on constructing a relationship between discharge and water level, while the discharge obtained by the FATS decomposes velocity and depth into two ratings according to the continuity equation. Generally, this work highlights the performance of FATS as a powerful and effective approach for continuous streamflow measurements at high-frequency levels.

Is language evolution grinding to a halt? The scaling of lexical turbulence in English fiction suggests it is not

Of basic interest is the quantification of the long term growth of a language's lexicon as it develops to more completely cover both a culture's communication requirements and knowledge space. Here, we explore the usage dynamics of words in the English language as reflected by the Google Books 2012 English Fiction corpus. We critique an earlier method that found decreasing birth and increasing death rates of words over the second half of the 20th Century, showing death rates to be strongly affected by the imposed time cutoff of the arbitrary present and not increasing dramatically. We provide a robust, principled approach to examining lexical evolution by tracking the volume of word flux across various relative frequency thresholds. We show that while the overall statistical structure of the English language remains stable over time in terms of its raw Zipf distribution, we find evidence of an enduring ‘lexical turbulence’: The flux of words across frequency thresholds from decade to decade scales superlinearly with word rank and exhibits a scaling break we connect to that of Zipf's law. To better understand the changing lexicon, we examine the contributions to the Jensen-Shannon divergence of individual words crossing frequency thresholds. We also find indications that scholarly works about fiction are strongly represented in the 2012 English Fiction corpus, and suggest that a future revision of the corpus should attempt to separate critical works from fiction itself.

Simulating clear-sky index increment correlations under mixed sky conditions using a fractal cloud model

Modelling clear-sky index increments (i.e. changes in normalized surface irradiance over specified intervals of time) and their spatial autocorrelation structures is important for the reliable grid integration of photovoltaic power systems. In order to capture increment correlation structures under mixed sky conditions, we apply a fractal cloud model. First, we use thousands of fish-eye sky camera and satellite images to estimate cloud edge fractal dimension D on scales between tens of meters and hundreds of kilometers. Box-counting analyses of cloud edges extracted from these images result in best-fit estimates of fractal dimension between 1.4 and 1.6, with satellite approximations being consistently higher than sky camera estimates. Contrary to previous studies, we find no evidence of any scale break and attribute the systematic discrepancy between the two estimates of D to intrinsic differences in the instrument-specific techniques of cloud detection. Next, we synthesize small-scale fractal cloud fields, with D=1.5 and satellite-derived cloud images as input. Using cloud motion vectors from the same satellite images, we then translate the small-scale cloud fields across a set of model pyranometer locations to obtain corresponding clear-sky index time series. From the simulated time series we calculate increment correlation structures for distances between tens of meters and about ten kilometers, and compare them to observation-based results from 1Hz measurements of up to 99 pyranometers. The observed isotropic, along-wind, and across-wind spatial autocorrelation structures of clear-sky index increments are captured well by the model, both in terms of overall value and shape. While there are some systematic differences between modelled and observed structures (e.g. underevaluation for very small time scales of a few seconds), the differences are essentially small. In general, the simulated correlations are not strongly sensitive to variations in the fractal model parameters.

Exploring the link between multiscale entropy and fractal scaling behavior in near-surface wind.

The equivalency between the power law behavior of Multiscale Entropy (MSE) and of power spectra opens a promising path for interpretation of complex time-series, which is explored here for the first time for atmospheric fields. Additionally, the present manuscript represents a new independent empirical validation of such relationship, the first one for the atmosphere. The MSE-fractal relationship is verified for synthetic fractal time-series covering the full range of exponents typically observed in the atmosphere. It is also verified for near-surface wind observations from anemometers and CFSR re-analysis product. The results show a ubiquitous β ≈ 5/3 behavior inside the inertial range. A scaling break emerges at scales around a few seconds, with a tendency towards 1/f noise. The presence, extension and fractal exponent of this intermediate range are dependent on the particular surface forcing and atmospheric conditions. MSE shows an identical picture which is consistent with the turbulent energy cascade model: viscous dissipation at the small-scale end of the inertial range works as an information sink, while at the larger (energy-containing) scales the multiple forcings in the boundary layer act as widespread information sources. Another scaling transition occurs at scales around 1–10 days, with an abrupt flattening of the spectrum. MSE shows that this transition corresponds to a maximum of the new information introduced, occurring at the time-scales of the synoptic features that dominate weather patterns. At larger scales, a scaling regime with flatter slopes emerges extending to scales larger than 1 year. MSE analysis shows that the amount of new information created decreases with increasing scale in this low-frequency regime. Additionally, in this region the energy injection is concentrated in two large energy peaks: daily and yearly time-scales. The results demonstrate that the superposition of these periodic signals does not destroy the underlying scaling behavior, with both periodic and fractal terms playing an important role in the observed wind time-series.

The breakdown of strength size scaling in spherical nanoindentation and microcompression of metallic glasses

It was previously reported that the strength of metallic glasses (MGs) would scale inversely with the size of a sample or a deformation field, commonly known as “smaller-being-stronger”. However, based on the extensive spherical nanoindentation experiments conducted across a variety of MGs, we demonstrate that such strength-size scaling breaks down at a critical indenter tip radius, which is caused by the transition of the yielding mechanism from bulk- to surface-controlled shear band initiation. Our experimental findings also provide an explanation for the unusual strength scattering observed in the micro-compression of MGs.

Mars topography investigated through the wavelet leaders method: A multidimensional study of its fractal structure

This work examines the scaling properties of Mars topography through a wavelet-based formalism. We conduct exhaustive one-dimensional (both longitudinal and latitudinal) and two-dimensional studies based on Mars Orbiter Laser Altimeter (MOLA) data using the multifractal formalism called Wavelet Leaders Method (WLM). This approach shows that a scale break occurs at approximately 15km, giving two scaling regimes in both 1D and 2D cases. At small scales, these topographic profiles mostly display a monofractal behavior while a switch to multifractality is observed in several areas at larger scales. The scaling exponents extracted from this framework tend to be greater at small scales. In the 1D context, these observations are in agreement with previous works and thus suggest that the WLM is well-suited for examining scaling properties of topographic fields. Moreover, the 2D analysis is the first such complete study to our knowledge. It gives both a local and global insight on the scaling regimes of the surface of Mars and allows to exhibit the link between the scaling exponents and several famous features of the Martian topography. These results may be used as a solid basis for further investigations of the scaling laws of the Red planet and show that the WLM could be used to perform systematic analyses of the surface roughness of other celestial bodies.

Multi-scale analysis of alpine landscapes with different intensities of abandonment reveals similar spatial pattern changes: Implications for habitat conservation

The abandonment of traditional anthropogenic activities is an important driver shaping landscape patterns. Therefore, multi-scale pattern analysis over time is needed to identify appropriate scales for biodiversity conservation and monitoring of abandoned landscapes. We compared spatial and temporal changes in a pair of alpine watersheds in Italy (Cajada and Tovanella), which are similar in size, geo-climatic conditions, and land-use histories; but have had divergent anthropogenic abandonment processes since the 1950s. We hypothesize that this divergence has led to corresponding dissimilarities in multi-scale patterns of landscape change. To examine this hypothesis, we analyzed land cover maps from three years (1954, 1980/83, 2006) and described the changes using transition matrices. For each year and watershed, landscape heterogeneity and a set of class-level metrics (i.e. percentage of the landscape, area-weighted mean patch size, patch density, area-weighted mean shape index, edge density, and aggregation index) were also measured at different scales using random sampling techniques, and the results were summarized by using scalograms. Woodland expansion occurred mainly at the expenses of grasslands, meadows, and shrublands. These changes were greater during the first time-period (1954-80/83) than in the more recent period (1980/83-2006), with a mean annual value that decreased from +5.18 to +1.33ha/year and from +4.08 to +1.96ha/year in the abandoned and managed watersheds, respectively. Landscape heterogeneity decreased over time with a similar pattern in both watersheds, which indicates a general process of homogenization. Management regime affected the spatial-scale response of class-level metrics; these metrics showed a variety of multi-scalar responses, which were not always consistent over time and under different management regimes. When considering the response of the indices across spatial-scales for both watersheds, certain historical curves showed a scale break, representing a significant change in the shape and slope of the curve (i.e. scale divergence). The presence of scale breaks in the scalograms can potentially reveal important thresholds for biodiversity. For example, grassland and meadow patch density at small spatial scales (<200m radius), which was found to be important for protected butterfly species, had a greater reduction over time in the managed watershed when compared to the abandoned watershed. In conclusion, the findings of this study indicate that there is good potential for understanding changes in landscape patterns under different management abandonment regimes by combining spatial and temporal analysis of class-level metrics.

Are there multiple scaling regimes in Holocene temperature records?

Abstract. The concept of multiple scaling regimes in temperature time series is examined, with emphasis on the question whether or not a monoscaling model with one single scaling regime can be rejected from observation data from the Holocene. A model for internal variability with only one regime is simpler and allows more certain predictions on timescales of centuries when combined with existing knowledge of radiative forcing. Our analysis of spectra from stable isotope ratios from Greenland and Antarctica ice cores shows that a scale break around centennial timescales is evident for the last glacial period, but not for the Holocene. Spectra from a number of late Holocene multiproxy temperature reconstructions, and one from the entire Holocene, have also been analysed, without identifying a significant scale break. Our results indicate that a single-regime scaling climate noise, with some non-scaling fluctuations on a millennial timescale superposed, cannot be rejected as a null model for the Holocene climate. The scale break observed from the glacial time ice-core records is likely caused by the influence of Dansgaard–Oeschger events and teleconnections to the Southern Hemisphere on centennial timescales. From our analysis we conclude that the two-regime model is not sufficiently justified for the Holocene to be used for temperature prediction on centennial timescales.

Contrasting scaling properties of interglacial and glacial climates.

Understanding natural climate variability is essential for assessments of climate change. This is reflected in the scaling properties of climate records. The scaling exponents of the interglacial and the glacial climates are fundamentally different. The Holocene record is monofractal, with a scaling exponent H∼0.7. On the contrary, the glacial record is multifractal, with a significantly higher scaling exponent H∼1.2, indicating a longer persistence time and stronger nonlinearities in the glacial climate. The glacial climate is dominated by the strong multi-millennial Dansgaard–Oeschger (DO) events influencing the long-time correlation. However, by separately analysing the last glacial maximum lacking DO events, here we find the same scaling for that period as for the full glacial period. The unbroken scaling thus indicates that the DO events are part of the natural variability and not externally triggered. At glacial time scales, there is a scale break to a trivial scaling, contrasting the DO events from the similarly saw-tooth-shaped glacial cycles.

Turbulent airflow above a full-scale macroporous material: Boundary layer characterization and conditional statistical analysis

Convective drying of macroporous materials is governed by the complex interaction between airflow above and into the material, the roughness of the air–material interface and the characteristics of the material pore system. In this study, we experimentally investigate this interplay in detail and at full-scale, using porous asphalt (PA) as a model material. The characteristics of the turbulent flow in the immediate vicinity of the material surface are studied with full-scale wind tunnel experiments at three flow speeds over two types of PA with different surface porosities and surface pore sizes, and are compared to similar measurements over a smooth and impermeable reference material. It is shown that, above a certain wall-normal distance, turbulence profiles can be scaled to make them independent of the flow speed. However, at low speed, the scaling breaks down due to a combination of organized turbulent structures of high intensity and a low turbulence background. No generally valid scaling applicable at all tested air speeds is found close to the surface, where drying occurs. Hence, realistic drying experiments must be performed at full scale and for the entire range of velocities of interest.

How long is a hillslope?

AbstractHillslope length is a fundamental attribute of landscapes, intrinsically linked to drainage density, landslide hazard, biogeochemical cycling and hillslope sediment transport. Existing methods to estimate catchment average hillslope lengths include inversion of drainage density or identification of a break in slope–area scaling, where the hillslope domain transitions into the fluvial domain. Here we implement a technique which models flow from point sources on hilltops across pixels in a digital elevation model (DEM), based on flow directions calculated using pixel aspect, until reaching the channel network, defined using recently developed channel extraction algorithms. Through comparisons between these measurement techniques, we show that estimating hillslope length from plots of topographic slope versus drainage area, or by inverting measures of drainage density, systematically underestimates hillslope length. In addition, hillslope lengths estimated by slope–area scaling breaks show large variations between catchments of similar morphology and area. We then use hillslope length–relief structure of landscapes to explore nature of sediment flux operating on a landscape. Distinct topographic forms are predicted for end‐member sediment flux laws which constrain sediment transport on hillslopes as being linearly or nonlinearly dependent on hillslope gradient. Because our method extracts hillslope profiles originating from every ridgetop pixel in a DEM, we show that the resulting population of hillslope length–relief measurements can be used to differentiate between linear and nonlinear sediment transport laws in soil mantled landscapes. We find that across a broad range of sites across the continental United States, topography is consistent with a sediment flux law in which transport is nonlinearly proportional to topographic gradient. © 2016 The Authors. Earth Surface Processes and Landforms published by John Wiley &amp; Sons Ltd.

An Unusual Dermatological Manifestation of Graves’ Disease

Abstract Introduction Pityriasis Rubra Pilaris (PRP) is a chronic inflammatory dermatological disease, the cause of it is not yet clear. Researchers have linked it to autoimmune disease, infections like HIV and streptococcal diseases. There was an established link hypothyroidism. This was significant in the view of some researchers to recommend thyroid function test (TFT) as part of PRP assessment. Case presentation We are presenting a 24-year old lady with a full picture of thyrotoxicosis (Grave’s disease). At the time of she started appreciating the symptoms of the thyrotoxicosis; she started feeling extensive skin dryness, scaling and skin breaks at the joints and the extensor surfaces. She sought dermatological advice in many centres, with no response. With the thyrotoxicosis treatment the skin jeopardy started to improve while she was only on emollients. The skin findings completely vanished after the radioactive iodine (RAI). Conclusions This was the first report of PRP in association with Grave’s disease. This link needs to be confirmed with more case reports. Vanishing skin changes with the thyroid settlement could make it part of the treatment of the PRP. This might strengthen the recommendation of the previous papers of adopting TFT as part of the PRP workup.

1/fnoise analyses of urbanization effects on streamflow characteristics

Nonstationary hydrologic behaviour resulting from rapid industrialization and urbanization, combined with climate change effects, likely produces greater challenges in water resources and flood risk managements. Our country-wide analyses for South Korea, based on spectral analysis technique, revealed how streamflow characteristics have shifted towards a less hydrologic memory state, which indicates a weaker temporal autocorrelation in the time series. Specifically, we analysed 1/fα noise of streamflow in 78 unit watersheds in five major river basins in South Korea to investigate the effects of urbanization on stream hydrologic responses over a 30-year period. The average slope of runoff spectra, α0, was 0.94 ± 0.20, indicating that runoffs are characterized by pink noise. The distribution of α0 showed a convergence towards <0.5 with increasing urbanization, indicating a clear effect of memory loss due to expanded impervious surface areas in watersheds. Among the watersheds examined, 59 showed bi-fractal scaling regimes, with scale break points located around 17.5 days. Analysis of the three spectral slopes, α0 (average), αL (in low-frequency domain), and αH (in high-frequency domain), revealed a threshold of urbanization ratio (UR) of ~15% from which all the three slopes decrease, and additional thresholds of UR around 6–7% are found from which all the three slopes increase as UR increases. While hydrologic responses of watersheds are the result of complex and compound interplay among many factors such as climate and topography, increasing urbanization seems to dominantly control the hydrologic properties resulting in homogenization of spectral slopes among various watersheds. Copyright © 2015 John Wiley & Sons, Ltd.