Surface Slope Measurements Research Articles

River Water Level and Water Surface Slope Measurement From Spaceborne Radar and LiDAR Altimetry: Evaluation and Implications for Hydrological Studies in the Ganga River

River Water Level and Water Surface Slope Measurement From Spaceborne Radar and LiDAR Altimetry: Evaluation and Implications for Hydrological Studies in the Ganga River

A New Reflected Target Optical Assessment System

NREL has completed stage 1 development of an indoor optical measurement tool for fully assembled heliostats and single facets. This tool began as an indoor version of NREL’s outdoor Non-Intrusive Optical (NIO) measurement technique [1]. It uses similar techniques to other available tools (deflectometry, photogrammetry, etc.), but is designed to require very little infrastructure, labor, and time to set up and collect surface slope and canting measurements, making it a valuable tool for quality assurance and laboratory measurement of heliostat optics. It accomplishes this by using computer vision, photogrammetry, and multiple images stitched together to minimize the printed target size and required setup precision. This adaptable setup is useful for taking measurements at a variety of heliostat pointing angles, and for measuring fully assembled heliostats on the assembly line. In this paper, we describe the methodology behind the measurement system, present an initial analysis of its uncertainty and sensitivity, and compare it with established optical measurement systems.

Interferometric metrology probe for highly sloped freeform optics.

A wide variety of systems are employed to measure the surface profile of aspheric and freeform optical surfaces. Freeform metrology systems must accurately characterize the full surface under test, which can be difficult with steep surface slopes. Here we present an interferometric surface metrology probe for highly sloped aspheric and freeform optical surfaces. The optical design of this probe allows the measurement of surface slopes up to 50deg without tilting the probe, which simplifies stage design and increases the accuracy of the system. A spectrally controlled light source is used to create a virtual ball in front of the probe tip to measure the surface distance and angle. This system produces a cloud of points, to which Zernike polynomials are fit and used to reconstruct the surface. We will show sensitivity tests and accuracy results.

Characterizing the Variability of a Physical Driver of North Atlantic Right Whale Foraging Habitat Using Altimetric Indices

Physical ocean circulation features, especially the Gaspé Current (GC) intrusion, influence the transport and aggregation of whale prey, thereby influencing the whale foraging habitat in the Gulf of St. Lawrence (GSL), Canada. We employ satellite altimetry-derived sea level anomaly (SLA) indices to monitor interannual variations in the intensity of the GC in the North Atlantic Right Whale (Eubalaena glacialis; NARW) habitat in the GSL. Measurements of surface slope and volume transport are taken from the SLA profiles along a repeating ground track of the Jason-2/3 satellites. These are employed as complementary proxies in characterizations of physical processes in the GSL. The relationship between altimetric indices and indices of zooplankton abundance are explored in the southern GSL. Results demonstrate that an altimetric index estimated from surface slope (Indexslope−half) is correlated with river discharge of the St. Lawrence River and can be utilized to infer variations in GC intensities. Time series of the altimetric indices during 2009–2021 are found to exhibit interannual and seasonal environmental variability, which influence transport into the southern GSL. As captured by the altimetric indices, these features of the surface ocean circulation can be linked to zooplankton variations in the Shediac Valley, where NARWs are frequently observed. Therefore, in linking physical drivers of ocean dynamics to the NARW foraging habitat, variations in these indices can also potentially help describe some features of the distribution patterns of NARW sightings in this area.

Fiber-Coupled Common-Path Shearography for Simultaneous Measurement of Surface Deformation and Slope

Fiber-Coupled Common-Path Shearography for Simultaneous Measurement of Surface Deformation and Slope

A Framework for Estimating Global River Discharge From the Surface Water and Ocean Topography Satellite Mission

AbstractThe Surface Water and Ocean Topography (SWOT) mission will vastly expand measurements of global rivers, providing critical new data sets for both gaged and ungaged basins. SWOT discharge products (available approximately 1 year after launch) will provide discharge for all river that reaches wider than 100 m. In this paper, we describe how SWOT discharge produced and archived by the US and French space agencies will be computed from measurements of river water surface elevation, width, and slope and ancillary data, along with expected discharge accuracy. We present for the first time a complete estimate of the SWOT discharge uncertainty budget, with separate terms for random (standard error) and systematic (bias) uncertainty components in river discharge time series. We expect that discharge uncertainty will be less than 30% for two‐thirds of global reaches and will be dominated by bias. Separate river discharge estimates will combine both SWOT and in situ data; these “gage‐constrained” discharge estimates can be expected to have lower systematic uncertainty. Temporal variations in river discharge time series will be dominated by random error and are expected to be estimated within 15% for nearly all reaches, allowing accurate inference of event flow dynamics globally, including in ungaged basins. We believe this level of accuracy lays the groundwork for SWOT to enable breakthroughs in global hydrologic science.

Ocean Wind Observation Based on the Mean Square Slope Using a Self-Developed Miniature Wave Buoy.

Real-time, continuous, and long-term marine monitoring data benefits ocean research. This study developed a low-cost, multi-parameter, miniature wave buoy. High spatial and temporal resolution of sea surface parameters, including wind, waves, and current, can be obtained at low cost through the deployment of numerous buoys, thus forming an observation array. Tested in the laboratory water tank, the relative error of water surface slope measurement of the buoy was approximately 5.6% when the slope angle was less than 15°. For frequencies between 0.1 and 1.0 Hz, the measurement of slope spectrum was almost identical to that of the wave gauge. The buoy underestimated the slope spectrum between 1.0–1.56 Hz. A good relationship (r2 = 0.75) was obtained between wind speed at 10 m above sea surface (U10) and the low-pass-filtered mean square slope (LPMSS). After incorporating the wave age into the U10 inversion process, the root mean square error (RMSE) and BIAS were reduced to 1.15 m/s and 0.02 m/s, respectively. The 2D distribution of buoy-measured slope components was used to detect the wind direction, with an RMSE of 23.7°. The spectral tail slope steepened with increasing wind speed at low wind speeds (<7 m/s). A technical flow chart of the miniature wave buoy is proposed to observe the sea surface parameters. This miniature buoy will play an essential complementary role in the growing demand for sea state monitoring, especially in nearshore oceans.

Exploring the potential of Sentinel-3 delay Doppler altimetry for enhanced detection of coastal currents along the Northwest Atlantic shelf

In this study, we evaluate Sentinel-3A satellite synthetic aperture radar (SAR) altimeter observations along the Northwest Atlantic coast, spanning the Nova Scotian Shelf, Gulf of Maine, and Mid-Atlantic Bight. Comparisons are made of altimeter sea surface height (SSH) measurements from three different altimeter data processing approaches: fully-focused synthetic aperture radar (FFSAR), un-focused SAR (UFSAR), and conventional low-resolution mode (LRM). Results show that fully-focused SAR data always outperform LRM data and are comparable or slightly better than the nominal un-focused SAR product. SSH measurement noise in both SAR-mode datasets is significantly reduced compared to LRM. FFSAR SSH 20-Hz noise levels, derived from 80-Hz FFSAR data, are lower than 20-Hz UFSAR SSH with 25% noise reduction offshore of 5 km, and 55–70% within 5 km of the coast. The offshore noise improvement is most likely due to the higher native along-track data posting rate (80 Hz for FFSAR, and 20 Hz for UFSAR), while the large coastal improvement indicates an apparent FFSAR data processing advantage approaching the coastlines. FFSAR-derived geostrophic ocean current estimates exhibit the lowest bias and noise when compared to in situ buoy-measured currents. Assessment at short spatial scales of 5–20 km reveals that Sentinel-3A SAR data provide sharper and more realistic measurement of small-scale sea surface slopes associated with expected nearshore coastal currents and small-scale gyre features that are much less well resolved in conventional altimetric LRM data.

Post-Processing Deflectometry Grid Images Using Particle Image Velocimetry Analysis

AbstractDeflectometry is a full-field optical technique for surface slope measurement based on recording the deformation of a grid image. A hybrid method is explored in which the grid images from a deflectometry measurement are processed using a particle image velocimetry analysis tool. The hybrid approach is compared to a common phase shifting algorithm for grid images based on a windowed discrete Fourier transform. The resulting slope maps compare well with those identified using the spatial phase shifting procedure. While the traditional phase shifting method has a tuning requirement that limits the optical setup to configurations that produce an integer number of pixels per grid period in the image, the use of particle image velocimetry analysis omits this calibration step. The applicability of an existing turnkey tool to perform full-field vibration imaging using deflectometry can benefit to research concerning mechanical vibration and related experimental methods.

A Drone‐Borne Method to Jointly Estimate Discharge and Manning's Roughness of Natural Streams

AbstractImage cross‐correlation techniques, such as particle image velocimetry (PIV), can estimate water surface velocity (v surf) of streams. However, discharge estimation requires water depth and the depth‐averaged vertical velocity (U m ). The variability of the ratio U m /v surf introduces large errors in discharge estimates. We demonstrate a method to estimate v surf from Unmanned Aerial Systems (UASs) with PIV technique. This method does not require any ground control point (GCP): the conversion of velocities from pixels per frame into length per time is performed by informing a camera pinhole model; the range from the pinhole to the water surface is measured by the drone‐borne radar. For approximately uniform flow, U m is a function of the Gauckler‐Manning‐Strickler coefficient (K s ) and v surf. We implement an approach that can be used to jointly estimate K s and discharge by informing a system of two unknowns (K s and discharge) and two nonlinear equations: i) Manning's equation and ii) mean‐section method for computing discharge from U m . This approach relies on bathymetry, acquired in situ a priori, and on UAS‐borne v surf and water surface slope measurements. Our joint (discharge and K s ) estimation approach is an alternative to the widely used approach that relies on estimating U m as 0.85·v surf. It was extensively investigated in 27 case studies, in different streams with different hydraulic conditions. Discharge estimated with the joint estimation approach showed a mean absolute error of 19.1% compared to in situ discharge measurements. K s estimates showed a mean absolute error of 3 m1/3/s compared to in situ measurements.

Surface wave spectral properties of centimeter to decameter wavelengths: variable spectral slope and non-equilibrium spectrum

Understanding the wave properties in centimeter to decameter (cmDm) wavelength range is of great interest to ocean remote sensing and air-sea interaction. For more than six decades, cmDm waves are generally considered to be in the equilibrium range, and its spectral function has a constant slope: − 5 or − 4 in the 1D frequency spectrum and − 3 or − 2.5 in the 1D wavenumber spectrum. Some variations of the equilibrium spectrum model include varying the frequency spectral slope from − 4 to − 5 at some multiple of the spectral peak frequency, or incorporating a threshold velocity in the reference wind speed. Extensive efforts are then devoted to quantifying the spectral coefficient of the equilibrium spectrum function. This paper emphasizes that the observed wave spectral slope in the ocean is mostly non-constant. Therefore, the wave properties in field observations are significantly different from those inferred from assuming a constant spectral slope. The variable spectral slope is indicative of a non-equilibrium nature of ocean surface waves. Furthermore, from signal-to-noise consideration, surface slope is much more suited than elevation for evaluating the spectral slope and for quantifying the cmDm wave properties. Microwave sensors are excellent instruments for providing the ocean surface slope measurements. Several large datasets of lowpass-filtered mean square slope (LPMSS) have been reported recently. Combining the LPMSS observations with a spectrum function that accommodates a variable spectral slope, several quantitative results on the variable spectral slope and cmDm wave properties are presented.

How will radar layover impact SWOT measurements of water surface elevation and slope, and estimates of river discharge?

Water surface elevation (WSE), slope and width measurements from the forthcoming Surface Water and Ocean Topography (SWOT) mission will enable spaceborne estimates of global river discharge. WSE will be measured by interferometric synthetic aperture radar (InSAR). InSAR measurements are vulnerable to contamination from layover, a phenomenon wherein radar returns from multiple locations arrive at the sensor simultaneously, rendering them indistinguishable. This study assesses whether layover will significantly impact the precision of SWOT estimates of global river discharge. We present a theoretical river layover uncertainty model at the scale of nodes and reaches, which constitute nominal 200 m and 10 km averages, respectively, along river centerlines. The model is calibrated using high-resolution simulations of SWOT radar interaction with topography covering a total of 41,233 node observations, across a wide range of near-river topographic features. We find that height uncertainty increases to a maximum value at relatively low values of topographic standard deviation and varies strongly with position in the swath. When applied at global scale, the calibrated model shows that layover causes expected height uncertainty to increase by only a modest amount (from 9.4 to 10.4 cm at the 68th percentile). The 68th percentile of the slope uncertainty increases more significantly, from 10 to 17 mm/km. Nonetheless, the 68th percentile discharge uncertainty increases only marginally. We find that the impact of layover on SWOT river discharge is expected to be small in most environments.

Spatial accuracy assessment of unmanned aerial vehicle-based structures from motion multi-view stereo photogrammetry for geomorphic observations in initiation zones of debris flows, Ohya landslide, Japan

Fluctuations in sediment storage arising from sediment discharge and recharge in headwater channels are an important factor influencing changes in landforms in mountainous areas, but the frequency of surveys is limited because of access difficulties and complex topography. Although unmanned aerial vehicle-based structure-from-motion photogrammetry (UAV-SfM) may be effective for topographic measurement, its utilization in headwater channels has not been fully examined. We assessed the accuracy and reproducibility of a digital elevation model acquired via UAV-SfM (DEMSfM) in a headwater channel within the Ohya landslide area, Japan, using a DEM acquired via terrestrial laser scanning (DEMTLS). The results indicate that differences in the measured elevation between DEMSfM and DEMTLS in the vicinity of the channel bed ranged from about 0.4 to −0.4 m, with a median of 0.06 m. Hence, the profiles acquired via DEMSfM coincide well with those acquired via DEMTLS, and the spatial distributions and histograms of the measured surface slope were nearly the same for UAV-SfM and TLS. However, part of the DEMSfM indicates low elevation compared with DEMTLS, probably because of topical distortion arising from technical problems in UAV-SfM. The positive and negative differences in volume between DEMSfM and DEMTLS were approximately 200 and −30 m3, respectively. To remedy this bias, an alignment of the UAV-SfM point cloud using the TLS point cloud in the hillslope sections was conducted, based on an iterative closest point (ICP) algorithm. Consequently, the median of the elevation differences decreased to −0.002 m, resulting in the positive and negative differences becoming approximately 100 m3. This demonstrates that ICP-based alignment can lead to a reduction of the deviation of differences in the estimated volume. In terms of eliminating biases due to topical distortion in elevation, this approach would be valid for the estimation of volumetric changes using UAV-SfM.

$L$ -Band Ocean Surface Roughness

Surface wave spectral properties of centimeter to decameter (cmDm) wavelengths are of great interest to microwave remote sensing of the ocean. They are obviously different from the high-frequency extension of the wind-wave spectrum models developed for ocean science and engineering applications, which focus on the longer waves in the energetic peak region of the wave spectrum. For more than six decades, the cmDm waves are generally considered to be in the equilibrium range, and its spectral function has a constant slope: −5 or −4 in the 1-D frequency spectrum, and −3 or −2.5 in the 1-D wavenumber spectrum. The observed wind-wave spectral slopes, however, are not constant. As a result, the cmDm wave properties are significantly different from those inferred from an equilibrium spectrum model. Surface slope measurements are more suited for studying the cmDm waves. Microwave radar backscattering cross sections have been used to study the shorter range of cmDm waves. L-band lowpass-filtered mean square slope (LPMSS) is contributed by waves longer than about 0.6 m, here referred to as the decimeter to decameter (dmDm) waves. The analysis of LPMSS has improved the modeling of dmDm waves. Ultimately, the spectral slope variation is a critical characteristic of cmDm waves. The wave spectrum model formulated with the variable spectral slope consideration produces very good agreement with L-band scatterometer and reflectometer measurements.

Reconstruction of surface-pressure fluctuations using deflectometry and the virtual fields method

This study presents an approach for obtaining full-field dynamic surface-pressure reconstructions with low differential amplitudes. The method is demonstrated in a setup where an air jet is impinging on a flat plate. Deformations of the flat plate under dynamic loading of the impinging jet were obtained using a deflectometry setup that allows measurement of surface slopes with high accuracy and sensitivity. The measured slope information was then used as input for the virtual fields method to reconstruct pressure. Pressure fluctuations with amplitudes of down to {mathcal {O}}(1)~text {Pa} were extracted from time-resolved deflectometry data using temporal band-pass filters. Pressure transducer measurements allowed comparisons of the results with an established measurement technique. Even though the identified uncertainties in fluctuations were found to be as large as 50%, the spatial distributions of dynamic pressure events were captured well. Dynamic mode decomposition was used to identify relevant spatial information that correspond to specific frequencies. These dynamically important spatio-temporal events could be observed despite their low differential amplitudes. Finally, the limitations of the proposed pressure determination method and strategies for future improvements are discussed.Graphic abstract

How will radar layover impact SWOT measurements of water surface elevation and slope, and estimates of river discharge?

How will radar layover impact SWOT measurements of water surface elevation and slope, and estimates of river discharge?

A simplified reflection-mode digital gradient sensing technique for measuring surface slopes, curvatures and topography

A simplified optical apparatus for reflection-mode Digital Gradient Sensing methodology (r-DGS) to perform full-field measurement of surface slopes is proposed. It eliminates the need for a beam splitter to record random speckles off a target and via the specular specimen normally. Instead, the target plane speckles reflected off the specimen surface are directly recorded at a known inclined angle. The simplification results in a highly efficient optical arrangement in terms of light loss intrinsic to the original apparatus that used a beam splitter. The simplified apparatus, however, requires altering the governing equations while interpreting the correlated speckle fields in the reference and deformed states. The details of these issues as well as successful demonstrations of simplified r-DGS to measure deflection of thin Si wafer subjected to flexure is reported. The modified approach is also demonstrated to study crack-tip deformations near an edge crack in a beam.

Steep Bedload‐Laden Flows: Near Critical?

Steep gravel‐bed rivers sometimes experience floods that dramatically rework river bed structure and topography. Hazard assessments and paleo‐event reconstructions require better knowledge of such phenomena. This paper explores morphodynamic evolution of steep channels carrying bedload‐laden flows, using a generic Froude‐scaled model. Bedload‐laden floods were introduced in a narrow flume and spread into a 5 times wider unconfined area with a 0.1 steep slope (m/m). Image analysis enabled measurements taken at an unprecedented level of accuracy on unconfined flows laden with bedload. A flow reconstruction procedure was used to compute depth, Froude (Fr) and Shields (τ*) numbers on millions of pixels based on a friction law and measurements of surface velocity, slope, and roughness. Despite the steep slope, Froude numbers proved to be mostly subcritical in all but the regions experiencing the most active sediment transport. Competent flows, identified by the transport stage higher than unity ( ), were near critical and seldom had Fr&gt; 1.3–1.5. This demonstrates that, providing that bed width and structure can adjust, hydraulic features such as standing waves, hydraulic jumps, and lateral shock waves dissipate energy very efficiently in addition to adjusting channel features. These competent flows also tend to rework channels to approach the energy minimum of near‐critical flows. This hypothesis was postulated by Gordon Grant (1997, https://doi.org/10.1029/96WR03134, Wat. Resour. Res. 33(2):349‐358) but demonstrated here for the first time at this scale. Considering near‐critical flows during discharges high enough to be clearly competent in laterally unconfined reaches seems reasonable as a first approximation in steep channels.

Infrared Deflectometry for Slope Deformation Measurements

This paper presents an implementation of deflectometry in the infrared spectrum. Deflectometry consists in recording the specular image of a reference grid pattern onto the mirror-like surface of a test specimen. This technique has two main advantages, high sensitivity and direct measurement of surface slopes, which in the case of thin plate bending is only one spatial differentiation away from surface strains. The objective of imaging in the infrared spectrum is to mitigate the main limitation of deflectometry in the visible spectrum, which is to require an extremely smooth surface to provide dominant specular reflection. This paper explores IR deflectometry for the first time for deformation measurements. Two different infrared cameras were assessed for use in IR deflectometry, a short wave quantum detector one, and a long wave microbolometer (MB) array one. Different materials of varying surface roughness were imaged and it was verified that the Rayleigh criterion was appropriate to determine whether IR deflectometry was feasible on a given surface. With the MB camera, most off-the-shelf material surfaces proved reflective enough to perform IR deflectometry. Finally, several bending tests were performed on aluminium plates and the deformation fields were shown to compare remarkably well with finite element simulations. The experimental data were then used in the Virtual Fields Method (VFM) and the elastic stiffness components of aluminium were retrieved with excellent accuracy, further validating IR deflectometry.

Reflection-mode digital gradient sensing method: measurement accuracy

Surface topography evaluation from measured surface slopes is critical in many engineering applications, including metrology of electronic substrates, optical elements, and small deformation measurement of engineering structures subjected to external thermomechanical stimuli. A recently proposed noncontact full-field optical method called reflection-mode digital gradient sensing (r-DGS) is able to measure small angular deflections of light rays proportional to two orthogonal surface slopes. It has been shown that submicron scale deformations can be detected by processing the slope data using a robust numerical integration scheme called the higher-order finite-difference-based least-squares integration. However, the smallest measurable deformations and the associated accuracy are yet to be determined. In our work, this very issue is addressed by carrying out experiments at temporally different recording frequencies, namely (a) ultrahigh-speed digital photography at 106 frames per second (fps) and (b) slow recording speeds of 101 fps. The results show that r-DGS is able to measure submicron out-of-plane deformations under latter conditions and nanoscale deformations in the former conditions.