Roughness Statistics Research Articles

Predicting flow resistance in rough‐bed rivers from topographic roughness: Review and open questions

AbstractMost ways of predicting flow resistance in shallow rivers with a partial or complete cover of coarse sediment use a bed‐sediment grain diameter as a roughness length scale. However, beds with the same grain size distribution differ in roughness and flow resistance depending on how the larger grains are arranged, the nature of any bedforms and the possible complications of bedrock or rough banks. This has led to interest in predicting flow resistance using metrics of the topographic roughness of the bed. Some researchers have used the standard deviation of bed elevation as a roughness length scale. An alternative for channels containing boulders is to regard the bed as an array of large roughness elements. Fluvial research to date using these two approaches is limited and inconclusive. We review potentially relevant findings from the much more extensive literature in boundary‐layer meteorology and various branches of engineering and note links between the distribution‐statistics and element‐array approaches. The skewness of the elevation distribution is widely seen as important but it is unclear how best to use it for flow prediction. Other open questions include the scale dependence of topographic metrics, and what type of flow resistance equation to use them in. Calibration and testing of new prediction methods require flow data from reaches with known roughness statistics. This need should be met partly by measurements at field sites or in flume models of them, but also by flume experiments and numerical simulations using synthetic roughness.

Rough surfaces in underexplored surface morphology space and their implications on roughness modelling

We report direct numerical simulations results of the rough-wall channel, focusing on roughness with high $k_{rms}/k_a$ statistics but small to negative $Sk$ statistics, and we study the implications of this new dataset on rough-wall modelling. Here, $k_{rms}$ is the root mean square, $k_a$ is the first-order moment of roughness height, and $Sk$ is the skewness. The effects of packing density, skewness and arrangement of roughness elements on mean streamwise velocity, equivalent roughness height ( $z_0$ ) and Reynolds and dispersive stresses have been studied. We demonstrate that two-point correlation lengths of roughness height statistics play an important role in characterizing rough surfaces with identical moments of roughness height but different arrangements of roughness elements. Analysis of the present as well as historical data suggests that the task of rough-wall modelling is to identify geometric parameters that distinguish the rough surfaces within the calibration dataset. We demonstrate a novel feature selection procedure to determine these parameters. Further, since there is no finite set of roughness statistics that distinguish between all rough surfaces, we argue that obtaining a universal rough-wall model for making equivalent sand-grain roughness ( $k_s$ ) predictions would be challenging, and that each rough-wall model would have its applicable range. This motivates the development of group-based rough-wall models. The applicability of multi-variate polynomial regression and feedforward neural networks for building such group-based rough-wall models using the selected features has been shown.

Linear Statistics of Determinantal Point Processes and Norm Representations

Abstract We study the asymptotic behavior of the fluctuations of smooth and rough linear statistics for determinantal point processes on the sphere and on the Euclidean space. The main tool is the generalization of some norm representation results for functions in Sobolev spaces and in the space of functions of bounded variation.

Surface roughness and wave slope statistics from the multi-spectral polarimetric imaging of the ocean surface.

The polarization of light in Ocean Color (OC) applications provides important information about atmospheric parameters, water composition, and the ocean surface. The Stokes vector components and the degree of linear polarization of light contain useful information about the air-water interface, including ocean surface roughness. We present polarimetric measurements and analysis of the ocean wave slopes at several bands. Data is acquired with a Teledyne DALSA camera, which uses a polarizer-on-chip focal plane of 1232 × 1028 super-pixels, where each pixel is made of four subpixels with 0-, 90-, 45- and 135-degrees orientation of polarization. We present a modified version of the Polarization Slope Sensing (PSS) technique [Zappa et al., 2008] for the non-contact detection of wave slopes and demonstrate a good performance of the updated algorithm in several conditions where the original technique was not applicable. Derived wave slopes are presented for various aquatic and atmospheric environments, including during VIIRS Cal/Val cruises and at a near-shore pier. The results are shown to be consistent with theoretical wave slope models.

Arctic Sea Ice Topography Information From RADARSAT Constellation Mission (RCM) Synthetic Aperture Radar (SAR) Backscatter

AbstractSea ice topography information can be obtained from altimetry but these data are spatially and temporally limited compared to recent synthetic aperture radar (SAR) missions such as the RADARSAT Constellation Mission (RCM). We analyze the relationship between sea ice roughness and height obtained from three Ice, Cloud, and Land Elevation Satellite (ICESat)‐2 tracks on two dates in March 2022, with RCM backscatter from 17 images in the McClintock Channel, Canadian Arctic. We analyze how this relationship varies with ice type, polarization, and incidence angle. We find particularly notable relationships between sea ice roughness and horizontal‐transmit/vertical‐receive backscatter for first‐year ice, and sea ice height and backscatter for multi‐year ice. We develop a preliminary model for winter sea ice roughness retrieval using RCM. In comparison with independent ICESat‐2 data in our study region, we find the model performs effectively at estimating a roughness distribution and key roughness statistics, and characterizes spatial variations in roughness at a sub‐kilometer scale.

Roughness Related to Cooling Performance of Channels Made Through Additive Manufacturing

Abstract The complex surface morphology and multiscale surface features inherent in additively manufactured (AM) components contribute to the overall flow characteristics and heat transfer of cooling passages. As the AM process and cooling data in the literature continue to evolve, so does the need for more accurate heat transfer and pressure loss correlations for AM cooling schemes. This study improves the predictability of pressure loss and heat transfer for AM cooling passages by fabricating a range of coupons and investigating samples in the literature. Twenty-seven test coupons were manufactured using direct metal laser sintering in an assortment of build directions and build locations that produced a variety of surface morphologies. Nondestructive evaluation, computed tomography scanning, was used to quantify the surface morphology as well as capture the as-built geometric dimensions of the cooling schemes. The friction factor and bulk Nusselt number of the coupons were measured using an experimental rig. Pressure loss and heat transfer correlations in the literature were compared with the experimental results from the current coupons and datasets from the literature. Arithmetic mean roughness correlations in the literature struggled to predict the cooling performance of AM channels since the bulk roughness statistic did not capture the overall form of the surface morphology. A combination of root mean square roughness and skewness of the roughness was able to best predict pressure loss and heat transfer for the present samples and those in the literature while being independent of build location, build direction, material, machine, and laser parameters. The maximum absolute error was 25% and the average absolute error was 12% for the friction factor correlation. The maximum absolute error was 39% and the average absolute error was 8% for the Nusselt Number correlation.

Prediction of equivalent sand-grain size and identification of drag-relevant scales of roughness – a data-driven approach

Despite decades of research, a universal method for prediction of roughness-induced skin friction in a turbulent flow over an arbitrary rough surface is still elusive. The purpose of the present work is to examine two possibilities; first, predicting equivalent sand-grain roughness size $k_s$ based on the roughness height probability density function and power spectrum (PS) leveraging machine learning as a regression tool; and second, extracting information about relevance of different roughness scales to skin-friction drag by interpreting the output of the trained data-driven model. The model is an ensemble neural network (ENN) consisting of 50 deep neural networks. The data for the training of the model are obtained from direct numerical simulations (DNS) of turbulent flow in plane channels over 85 irregular multi-scale roughness samples at friction Reynolds number $Re_\tau =800$ . The 85 roughness samples are selected from a repository of 4200 samples, covering a wide parameter space, through an active learning (AL) framework. The selection is made in several iterations, based on the informativeness of samples in the repository, quantified by the variance of ENN predictions. This AL framework aims to maximize the generalizability of the predictions with a certain amount of data. This is examined using three different testing data sets with different types of roughness, including 21 surfaces from the literature. The model yields overall mean error 5 %–10 % on different testing data sets. Subsequently, a data interpretation technique, known as layer-wise relevance propagation, is applied to measure the contributions of different roughness wavelengths to the predicted $k_s$ . High-pass filtering is then applied to the roughness PS to exclude the wavenumbers identified as drag-irrelevant. The filtered rough surfaces are investigated using DNS, and it is demonstrated that despite significant impact of filtering on the roughness topographical appearance and statistics, the skin-friction coefficient of the original roughness is preserved successfully.

Direction finding of electromagnetic radiation sources using the volumetric phased arrays consisting of the small number of elements

Problem statement. This article proposes a method to measure the bearing of electromagnetic radiation sources in the conditions of passive interference with multipath propagation and in the conditions of using "rough" (small number of elements) statistics taking into account particular design features of the direction finder located on a mobile object. The technical design of an adaptive direction finder (ADF) with a small number of channels M = 7 and “short spatial samples” m = 2 (bases) is substantiated, which leads to reducing hardware and software costs. Target. Determine the method of direction finding of electromagnetic radiation sources by volumetric phased arrays consisting of the small number of elements, which allow for the presence of passive interference with multipath radiation of electromagnetic radiation sources, and include spatial digital filters (DF) of a low order r = 2. Results. The problem of measuring the bearing of electromagnetic radiation sources under the conditions of correlated multipath passive interference and limited hardware and computing resources was solved. Direction finder includes a 7-element monopulse direction finder, which was built according to a sequential scheme at the nodes of a volumetric hexagonal grid with an equivalent spatial quantization step of 0.5l, forming programmable small-sized bases with a size of no more than l using the method of multiplexing (HF switching). Practical significance. The relevance of the proposed approach is substantiated due to the need to notch "multipath components", parasitic reflections from local objects surrounding the adaptive direction finder, and reduce the instrumental error in bearing measurement. A new approach to the construction of a volumetric phased array of an adaptive direction finder is proposed. Novelty. The synthesis of the optimal estimate is based on the principle of “whitewashing” passive correlated interference and the maximum likelihood method, which guarantees the achievement of potential direction finding accuracy in the conditions of using rough statistics that reduce hardware and software costs.

Characterization of the Blast Furnace Burden Surface: Experimental Measurement and Roughness Statistics

This paper is the first of a series of papers on the roughness characteristics of the burden surface in the blast furnace. The measurement method of the burden surface roughness texture is described, and the overall roughness characteristics of the burden surface are studied from a statistical point of view. This study focuses on two typical granularized burden materials, coke and sintered ore, which present four kinds of burden particles under two individual particle sizes. Simulated cold-state burden belts proportional to the practical burden radial sectors were stacked in a pilot plant. An RGBD camera was used to measure the simulated burden belt surfaces to obtain the surface texture details. Four corresponding digital elevation models of the burden belts were obtained through data processing. The root mean squared height, skewness, kurtosis, and spatial autocorrelation function are selected as statistical indexes. The obtained digital elevation models were counted. The results show that all four kinds of burden surfaces are Isotropic-Rough-Surface. In addition, the height distributions of the rough burden surface are close to the Gaussian distribution. Also, the spatial autocorrelation functions of the coke and large-sized sintered ore burden surfaces are close to the Gaussian function form. And lastly, the spatial autocorrelation function of the small sintered ore burden surface is close to the exponential function form.

An alternative to Hapke’s macroscopic roughness correction

In this paper, we present an alternative to Hapke’s correction for the photometric effect of macroscopic roughness of planetary surfaces (Hapke, 1984). Our model includes the effects of both single-facet scattering and multi-facet scattering. The single-facet scattering model is derived directly from the definition of bidirectional reflectance of a rough surface. We model projected shadowing by adopting an approximation published elsewhere in the literature. Monte Carlo simulations of single-facet scattering demonstrate very good agreement with the single-facet scattering component of our model. Using 3D printed molds with known roughness statistics, we prepared rough mineral surfaces consisting of quartz and olivine in the laboratory. We recorded extensive measurements of the rough surface bidirectional reflectance over a wide range of illumination and view geometries at 1751 wavelength bands ranging from 500–2250 nm. By fitting the residual between the measured bidirectional reflectance and our single-facet scattering model, we developed an empirical approximation for multi-facet scattering. Our results show that the multi-facet scattering is proportional to the surface’s diffusive reflectance, RMS slope, and the cosine of the illumination angle. Furthermore, the multi-facet scattering is approximately Lambertian for phase angles less than 90° but becomes forward scattering at higher phase angles. Our empirical multi-facet scattering model incorporates all of these features. As a surface becomes more macroscopically rough, our data show that the overall reflectance distribution becomes progressively more backscattering in a way that is distinct from the shadow hiding opposition effect. We refer to this effect as the macroscopic roughness backscattering bias (MRBB), which affects the entire hemisphere rather than being localized to small phase angles. Our proposed model is more accurate than Hapke’s for phase angles less than 90°, and the accuracy of the two models is comparable at higher phase angles. However, researchers should be aware of an issue regarding the roughness parameter defined in Hapke’s model, namely the fact that “ϑ¯” is not actually equal to the mean slope angle of the surface for the probability density function used in the model. This is an issue which apparently has gone unnoticed in the literature, and has potentially caused the model to be applied incorrectly in past studies.

The impact of non-Gaussian height distributions on the statistics of isotropic random rough surfaces

The impact of non-Gaussianity on the statistical geometry of isotropic random rough surfaces is analysed in this contribution. The non-Gaussian height distribution is modeled using the Weibull probability distribution. The summits height distribution, expected mean curvature and density of summits are obtained and compared with analytical solutions given by Nayak’s theory for the Gaussian case. A significant deviation from the Gaussian cases is observed. The mean curvature of negatively-skewed surfaces is found to decrease with the increase of height, contradicting the trend registered for the Gaussian case. Nayak’s parameter globally dominates the impact of the spectral properties. However, the wavelength ratio and the Hurst exponent are required to characterize the effect of the spectrum on the rough surfaces statistics.

Hyperspectral Image Classification Based on Multiscale Cross-Branch Response and Second-Order Channel Attention

Recently, most convolutional neural network-based methods use convolutional kernels of fixed size to extract features, which ignore the inherent spatial structure information of ground objects and lose spatial details. In addition, rough first-order statistics is not enough to capture subtle differences between different categories and extract non local context information. To address these issues, a hyperspectral image (HSI) classification method based on multi-scale cross-branch response and second-order channel attention (MCRSCA) is proposed in this paper. Firstly, a multi-scale cross-branch response module (MCBR) is proposed, which uses convolution kernels of different sizes for feature extraction. It adds and concatenates the features of different scales respectively to obtain rich and complementary spatial context information. Then, element multiplication and element addition are performed on the fused multi-scale features to promote the propagation of the multi-scale information and enhance the nonlinear expression ability. Next, the second-order channel attention module (SOCA) is designed to interact the channel information through the feature covariance matrix to obtain the long-term dependence between channels. This module pays more attention to the significant channels and suppresses the redundant channels. Finally, the residual connection is used to embed MCBR and SOCA into the residual block to improve the gradient back propagation and accelerate the training process. Experiments on four commonly used HSI benchmark datasets show that the results of MCRSCA is competitive compared with other state-of-the-art methods.

Old Plastic Bags conversion to Construction Bricks

One of the biggest constrains to manage solid waste is to tackle old plastic bags /shoppers. Their decomposition period ranges 10 to 10,000 years in rough statistics. To eliminate these bags from waste stream is a notorious difficulty. So to convert this problem to a product could be a fascinating approach. It is a forward step towards green behavior. It also minimizes dumping loads so it is a space safety measure as well.

Absorption and scattering by structured interfaces in X-rays

Promising achievements of resonance inelastic X-ray scattering and other spectroscopy studies in the range from hard X-ray to extreme ultraviolet require the development of exact tools for modeling energy characteristics of state-of-the-art optical instruments for bright coherent X-ray sources, space science, and plasma and superconductor physics. Accurate computations of the absorption and scattering intensity by structured interfaces in short wavelength ranges, i.e. realistic gratings, zone plates and mirrors, including multilayer-coated, are not widely explored by the existing methods and codes, due to some limitations connected, primarily, with solving difficult problems at very small wavelength-to-period (or to correlation length) ratios and accounting for random roughness statistics. In this work, absorption integrals and scattering factors are derived from a rigorous solution of the vector Helmholtz equations based on the boundary integral equations and the Monte Carlo method. Then, using explicit formulae (in quadratures), the author finds the absorption and scattering intensity of one- and bi-periodic gratings and mirrors, which may have random roughnesses. Examples of space and spectral power distributions for gratings and mirrors working in X-rays are compared with those derived using the usual indirect approach and well known approximations.

High Temperature Sealing of Silicon Oxide/Oxide Bonding Interfaces

High temperature (>1000°C) annealing is necessary to completely close a bonding interface. Using interface synchrotron high energy X-ray reflectivity, we have investigated the sealing behavior of silicon thermal oxide/ silicon thermal oxide interfaces, with different surface roughnesses. Interface X-ray reflection is able to measure accurately the width and the depth of the electron density gap across a bonding interface with a sub-nanometer accuracy, whose product is a good marker of the interface closure.The uncomplete closure of the interface is the result of a balance between attractive and repulsive force between the two bonded solids. These two forces depend on the statistics of asperity and on the mechanical behavior of individual asperity [1]. For attraction, at high temperatures, a key factor is the gain of contact surface area which reduces the surface energy due to uncontacted zones. Repulsion is due to compression of contacting asperities. At high temperature, both elastic and plastic behavior can be expected, with some yield of the asperities compressed above the elastic limit.In the elastic solid regime, we have shown that equilibrium distance of rough silicon oxide to rough siliconoxide bonding can be predicted using standard adhesive contact models such as Johnson-Kendall Roberts (JKR) or Deryagin-Müller-Toporov (DMT) with Gaussian roughness statistics[2]. The equilibrium distance is dependent and sensitive to the Fuller Tabor adhesion parameter, θ=E σ3/2 R1/2 / 2γR where E is the Young modulus, σ the mean roughness, R the radius of the asperity, while 2γ is the adhesion energy at contact points. When θ>>1 , the equilibrium distance is large and the contact area is small (unclosed interface) . When θ<<1 the adhesion energy is strong and the system will have a strong tendency to seal.In the plastic regime, both repulsive and attractive curves share the same dependence with distance so that the system is expected to be unstable, between a weakly evolving unsealed interface and a fully sealed interface when the asperity pressure stress is above the elastic limit.The kinetics of the sealing can also be modeled in this case, monitoring the interfacial gap as a function of time (Figure). It is found that the sealing characteristic time scales directly with the silicon oxide viscosity (Figure insert). This dependence can be understood using the plastic asperity contact model, assuming the fluid part flows according to the Stokes equation around asperities.

Effects of medium heterogeneities on direction of arrival estimation

A scaled experiment in a water tank was conducted to study effects of medium heterogeneities on underwater acoustic propagation while controlling the so-called fluctuations. An ultrasonic wave is transmitted (a pulse train at center frequency f = 2.25 MHz) throughout an acoustic lens presenting a plane input face and a randomly rough output face inducing spatial fluctuations of the sound pressure field. The roughness statistics are tuned so that the fluctuating pressure field presents features comparable to what can be observed in the case of acoustic waves propagating through a fluctuating ocean. Generally speaking, disturbances can include path propagation delays, multipath dependent Doppler spreading, scattering from the sea surface or bottom, and coherence loss over the array aperture arising from dynamic wave-front fluctuations due to internal waves. This last topic is the main focus of our study. Signal snapshots received at a virtual, vertical line array of 64 sensors may be corrupted by impulsive (heavy-tailed) additive noise and high resolution outlier-resistant arrival angle identification is desirable. Recent advances in robust techniques such as Sparse Bayesian Learning and L1 -norm Principal Component Analysis motivate this work. We compare the performance of these innovative techniques to the classical MUSIC and Bartlett processors. [This work is supported by DGA, NSF Grant CNS1753406, ONR.]

A New Representative Sampling Method for Series Size Rock Joint Surfaces

The greatest variability in both shear strength and roughness exists for joint samples with smaller size, which underscores the necessity of performing representative sampling. This study aims to provide a representative sampling method for series size joint surfaces. The progressive coverage statistical method is introduced to provide the sufficient sample capacity for series sampling sizes by setting different propulsion spaces. The statistical law of the joint surface morphology at different sampling sizes is measured by the 3D roughness parameter with {{theta }}_{max }^{ast }/({C}+1). Through an application in nine natural large-scale rock joints, nine consecutive sampling sizes from 100 mm × 100 mm to 900 mm × 900 mm are selected and 121 samples are successfully acquired from each sampling size. According to the frequency distribution of roughness statistics, a new sampling method combining the layering principle and K-medoids clustering algorithm is proposed to screen representative joint samples for each sampling size. The sampling results that meet the test accuracy requirements suggest the possibility of realizing an intelligent sampling method. In addition, the representative of the interlayer cluster center is validated. Finally, the comparison results with the traditional stratified sampling method prove that the proposed method has better stability.

What’s Important: Patience in Patients’ Care

What’s Important: Patience in Patients’ Care

Co‐evolution of coarse grain structuring and bed roughness in response to episodic sediment supply in an experimental aggrading channel

ABSTRACTWe use flume experiments to better understand how gravel‐bed channels maintain bed surface stability in response to pulses of sediment supply. Bed elevations and surface imagery at high spatial resolutions were used to quantify the co‐evolution of surface grain‐size distribution (GSD), bed roughness statistics, and bed surface structures (clusters, cells and transverse features). Using a new semi‐automated method, we identified individual stone structures over a 2 m × 1 m area throughout the experiments. After an initial coarsening, surface GSD and armouring ratio remained nearly stable as sediment pulses caused net bed aggradation. In contrast, individual grain structures continued to form, increase or decrease in size, and disappear throughout the experiments. The response of the bed to sediment pulses depended on the history of surface roughness evolution and bed surface structure development, as these factors changed much more in response to supply perturbations earlier in the experiments compared to later, even as the bed continued to aggrade. We interpret that the dynamic production and destruction of bed surface structures can act as a ‘buffer’ to sediment supply pulses, maintaining a stable bed surface during aggradation with minimal change in grain size or armouring. © 2019 John Wiley &amp; Sons, Ltd.

A model for roughness statistics of heterogeneous fibrous materials

We present a theory giving the standard roughness metrics R_{mathrm{a}} and R_{mathrm{q}} of stochastic fibrous materials in terms of their porosity and the thickness of the constituent fibres. Our treatment shows also that R_{mathrm{a}} and R_{mathrm{q}} are linearly dependent on each other with gradient depending on the skewness of the surface depth profile. Comparison of our theory with experiments on laboratory-formed paper samples and with data from the literature for industrially manufactured paper and carbon fibre nonwovens for use in fuel cells is excellent. The theory has applicability to generic families of stochastic fibrous materials and has relevance, for example, to printing of devices on paper.