Local Height Research Articles

Accurate estimation of lake levels by the spatio-temporal modeling of satellite altimetry data

Satellite altimetry is currently one of the most widely used techniques for monitoring lake water levels. Raw altimetry measurements are generally delivered in an ellipsoid height system, while lake heights are finally required in a local level height system to ensure the lake surface being strictly flat under the physical constraints of both gravity and non-gravity factors. Therefore, there is always a need for height system transformation of altimetry data. Many of the previous studies have used orthometric heights in an approximate manner in the altimetric data processing. The geoid errors, together with other error sources, can introduce significant biases into water level estimations. In this paper, we propose a spatio-temporal regression method to calculate orthometric height to level height (O2L) differences, which can be used to yield accurate lake levels from satellite altimetry data. In the experiments conducted in this study, we chose ICESat-2 data to train the O2L bias correction model, and evaluated the algorithm performance on two large lakes in central Asian (Issyk-Kul and Baikal lakes) and one lake in North America (Lake Michigan). The experimental results indicate that the spatio-temporal modeling method performs better than the traditional spatial modeling method in terms of regression accuracy, and the water levels derived from the new method are much closer to in-situ gauging measurements. Influenced by O2L bias, there is often a jitter phenomenon in the time series of lake levels, and the results of different satellites are, accordingly, not mutually consistent. A visual analysis reveals that the spatio-temporal modeling method can greatly reduce the high-frequency bias.

Unification of a Global Height System at the Centimeter-Level Using Precise Clock Frequency Signal Links

The International Association of Geodesy (IAG) aims to establish the International Height Reference System (IHRS) as one of its primary scientific objectives. Central to the realization of the IHRS is global vertical datum unification, which requires the connection of existing local vertical height reference systems (VHS) robustly and consistently. However, conventional methods are not suitable for estimating the offsets between two distant local height systems. In this paper, we propose a framework for connecting two local VHSs using ultraprecise clock frequency signal links between satellites and ground stations, referred to as the satellite frequency signal transmission (SFST) approach. The SFST approach allows for the direct determination of the geopotential and height differences between two ground datum stations without any location restrictions between the two VHSs. The simulation results show that the VHSs of China and the US can be unified with an accuracy of several centimeters, provided that the stability of atomic clocks used on-board the satellite and at on-ground datum locations reaches 4.8×10−17τ−1/2 for an averaging time τ (in seconds). We conclude that the SFST approach shows promise for achieving centimeter-level accuracy in unifying the global vertical height datum and represents a new paradigm for the realization of the IHRS.

Linkage of Normal Heights Obtained from GNSS and Refined XGM2019 GGM to Brazilian Vertical Data Using Different Approaches

This work aimed to analyze the use of different approaches to link normal heights obtained via Global Navigation Satellite System (GNSS)/Global Geopotential Model (GGM) refined by the RTM technique to the Brazilian Vertical Data (Imbituba Brazilian Vertical Datum – IBVD and Santana Brazilian Vertical Datum – SBVD). Specifically, it analyzed approaches based on the weighted mean of discrepancies between height anomalies, the zero- level geopotential value, the Geodetic Boundary Value Problem (GBVP) solution, and the use of parametric modeling of a plane with a scale factor. For the numerical tests, two different study regions have been used, the first with heights referenced to IBVD and the second to SBVD. Using the first three approaches, the local modeling idea has been investigated in both regions. In this context, spatial cluster analysis of the outliers of differences between local and global height anomalies defined the sub-regions. In the fourth approach, the treatment of local modeling was initially considered. In the accuracy analysis of linkages, it has been verified that approaches based on the mean of the discrepancies between height anomalies and using zero- level geopotential value propose practically the same results. On the other hand, there were improvements at the centimeter level with the use of the GBPV solution-based approach compared to the first two, except for two worsening cases. With the approach based on parametric modeling, the accuracy results were mainly worse considering the approaches with local modeling. The most significant differences reached the decimeter level.

Characteristics of the Oceanic Ambient Seismic Noise Around Tristan da Cunha in the South Atlantic From OBS Data

AbstractIt has long been recognized that specific ambient seismic noise is generated within the ocean. Therefore, ocean bottom seismometers have advantages to reveal the noise characteristics directly in the deep sea. We use the seismic recordings around Tristan da Cunha collected by 20 OBSs and two island stations to investigate the ambient noise sources in the middle of the South Atlantic. We analyzed the power spectral density, ambient noise cross‐correlations, and correlations with wave heights model. While primary microseisms (∼10–20 s) in this region are deficient, the secondary microseisms are strong and dominate the ambient noise at periods of ∼1–10 s, with the peak broadening to shorter periods (1–3 s). The secondary microseisms are strongly correlated with the local wave heights, especially at shorter periods (∼1–3 s), suggesting that the microseisms are affected mostly by local wave interactions. We observed clear Empirical Green's functions at periods of ∼3–10 s, indicating the existence of distant sources of secondary microseisms. Results of asymmetry analysis of cross‐correlations suggest the prominent direction of the distant source should be located to the Southwest and show barely seasonal variations. The correlations with wave heights indicate a possible source region in the southeast Pacific Ocean. Therefore, besides the dominating local wave‐wave interactions, the secondary microseisms around Tristan region are affected simultaneously by persistent distant sources from the deep basin in the Southeast Pacific Ocean, which might be related to the intense wave‐wave interactions caused by the blocking effect of the Drake Passage on ocean currents and waves.

Quadratic Chabauty for modular curves: algorithms and examples

We describe how the quadratic Chabauty method may be applied to determine the set of rational points on modular curves of genus $g>1$ whose Jacobians have Mordell–Weil rank $g$. This extends our previous work on the split Cartan curve of level 13 and allows us to consider modular curves that may have few known rational points or non-trivial local height contributions at primes of bad reduction. We illustrate our algorithms with a number of examples where we determine the set of rational points on several modular curves of genus 2 and 3: this includes Atkin–Lehner quotients $X_0^+(N)$ of prime level $N$, the curve $X_{S_4}(13)$, as well as a few other curves relevant to Mazur's Program B. We also compute the set of rational points on the genus 6 non-split Cartan modular curve $X_{\scriptstyle \mathrm { ns}} ^+ (17)$.

The impact of spume droplets induced by the bag-breakup mechanism on tropical cyclone modeling

Spume, large-radius seawater droplets that are ejected from the ocean into the atmosphere, can exchange moisture and heat fluxes with the surrounding air. Under severe weather conditions, spume can substantially mediate air-sea fluxes through thermal effects and thus needs to be physically parameterized. While the impact made by spume on air-sea interactions has been considered in bulk turbulent air-sea algorithms, various hypotheses in current models have resulted in uncertainties remaining regarding the effect of spume on air-sea coupling. In this study, we extended a classic bulk turbulent air-sea algorithm with a “bag-breakup” physical scheme of spume generation parameterizations to include spume effects in a complicated numerical model. To investigate the impact of spume on air-sea coupling, we conducted numerical experiments in a simulation of Tropical Cyclone Narelle. We observed a significant improvement in the ability to model minimum central pressure and maximum sustained surface wind speed when including the bag-breakup spume scheme. In particular, the impact of the bag breakup–generated spume is observed in the intensity, structure, and size of the tropical cyclone system through the modulation of local wind speed (U10), wave height (Hs), and sea surface temperature.

Guided Bone Regeneration in a Periodontally Compromised Individual with Autogenous Tooth Bone Graft: A Radiomics Analysis.

Autogenous tooth bone graft material (AutoBT) has been advocated as a bone substitute when conducting alveolar ridge preservation. This study is aimed at using a radiomics approach in order to evaluate and testify whether AutoBT can stimulate bone growth during socket preservation in severe periodontal cases. For this study, 25 cases with severe periodontal diseases were selected. The patients' AutoBTs were inserted into the extraction sockets and covered with Bio-Gide® collagen membranes. 3D CBCT scans and 2D X-rays were taken of the patients before surgery and after 6 months post-surgery. For the retrospective radiomics analysis, the maxillary and mandibular images were compared in different groups. Maxillary bone height was analyzed at the buccal, middle, and palatal crest sites, while the mandibular bone height was compared at the buccal, center, and lingual crest sites. In the maxilla, the alveolar height was increased by -2.15 ± 2.90 mm at the buccal crest; -2.45 ± 2.36 mm at the center of the socket, and -1.62 ± 3.19 mm at the palatal crest, while the height of the buccal crest was increased by 0.19 ± 3.52 mm, and the height at the center of the socket was increased by -0.70 ± 2.71 mm in the mandible. The three-dimensional radiomics analysis demonstrated significant bone growth in the local alveolar height and high density. Based on clinical radiomics analysis, AutoBT could be used as an alternative bone material in socket preservation after tooth extraction in patients with severe periodontitis.

Engineering of Nanoscale Heterogeneous Transition Metal Dichalcogenide-Au Interfaces.

Engineering the transition metal dichalcogenide (TMD)-metal interface is critical for the development of two-dimensional semiconductor devices. By directly probing the electronic structures of WS2-Au and WSe2-Au interfaces with high spatial resolution, we delineate nanoscale heterogeneities in the composite systems that give rise to local Schottky barrier height modulations. Photoelectron spectroscopy reveals large variations (>100 meV) in TMD work function and binding energies for the occupied electronic states. Characterization of the composite systems with electron backscatter diffraction and scanning tunneling microscopy leads us to attribute these heterogeneities to differing crystallite orientations in the Au contact, suggesting an inherent role of the metal microstructure in contact formation. We then leverage our understanding to develop straightforward Au processing techniques to form TMD-Au interfaces with reduced heterogeneity. Our findings illustrate the sensitivity of TMDs' electronic properties to metal contact microstructure and the viability of tuning the interface through contact engineering.

Vertebral Augmentation in Spine Surgery.

Vertebral augmentation has been a well-studied adjunct percutaneous procedure in spine surgery. Cement augmentation has been used in the treatment of compression fractures through kyphoplasties or vertebroplasties. Historically, data have shown no difference between treating compression fractures conservatively versus with percutaneous cement augmentation procedures. Recent literature has shown improvement in patient outcomes and increase in mobility with percutaneous cement augmentation procedures. Cement augmentation has been used in treating patients with spinal column fractures in higher energy trauma. Cement augmentation has shown to have a reduction in local kyphosis, improved pain, and significant height restoration of the anterior column in patients with burst fractures. Augmentation has been used in spinal deformity surgery, specifically to attempt to reduce the risk of proximal junctional kyphosis and to decrease the risk of screw pullout with cement augmented fenestrated screws in patients with osteoporosis. In pathologic compression fractures, cement augmentation is a safe, viable intervention to improve pain control in these patients. This review will go into the new advances of vertebral augmentation and indications for use in treatment today.

Experimental Study on the Stability and Wave Force of a Breakwater Transition under Multiangle Oblique Waves

Based on the failure and instability of different structural transitions of offshore breakwater, this paper provides a basis for understanding the instability mechanism and also provides suggestions for engineering repair. Based on the breakwater project in the regulation of the bay of Shandong Province, physical model tests with a scale of 1:36 were carried out. This study revealed the wave characteristics, the force performance, and the instability mechanism in the transition. In the test, the relationships between 5°, 15°, 35°, and 75° oblique waves, the wave force, and the stable weight of the Accropode were simulated, revealing that the generation of a shock wave current is related to the wave direction angle, which results in the local wave height increasing by 2.05 times. The result that the design weight of the armour block is unstable and stable after optimization is obtained. The wave force of the caisson of the transition was concentrated in the anti-arc section of the superstructure, and the maximum horizontal force, buoyancy force, and impact pressure were 935.6 kN, 419.1 kN, and 65.9 kPa, respectively. The instability mechanism was determined as the poor connection between the accropode and the caisson, and the wave energy concentration. Compared with the calculation results of the standard formula, the correction coefficients of the overtopping volume, the wave crest elevation, the wave force, and the Accropode weight at the transition of breakwater were 1.95, 1.97, 1.60, and 4.0, respectively. The test results have solved the practical problems of the project and can also provide a reference for similar projects.

A replacement model to simulate the nonlinear dynamics of electro-responsive liquid crystal coatings

An electric circuit replacement model is proposed to simulate the key nonlinear dynamics of electro-responsive liquid crystal polymer networks (LCNs). LCNs are known for having great potential to be integrated into smart functional surfaces due to their ability to generate various surface patterns. However, due to their complex molecular dynamics, low-order dynamic models that can accurately describe and predict their dynamic behavior are still lacking. In light of this research gap, we develop a lumped-parameter replacement model based on the observed dynamics in the experimental data and the physics of LCN dielectric properties. The unique assembly of lumped parameters in its simplest form describes the transformation of a high-frequency input voltage to a relatively slow increase in the local height of the LCN coating in between the electrodes, serving as an excitation mechanism to induce height change. The nonlinear dynamics of this height increase, as a function of both excitation frequency and voltage, is described by the proposed model. Furthermore, the comparison of the simulation results with the experimental data from LCN shows that key LCN response characteristics are captured well by the model. This model makes it possible to accurately predict and control the response of the electro-responsive LCN surfaces to obtain a predefined desired deformation pattern, which is a vital requirement for integrating them in haptic and smart surface devices.

Wave propagation in a circular channel: sloshing and resonance

Surface wave resonance of a liquid (water) layer confined in a circular channel is studied both experimentally and numerically. For the experiment, eight unevenly distributed ultrasonic distance sensors measure the local height of the wave surface. The resonance curves show maxima only for odd multiples of the fundamental resonance frequency f_0. We explained this behavior using a simple intuitive “ping-pong” like model. Collision of wave fronts can be observed for higher frequencies. Also, the wave reflection on the walls can be treated as wave collision with itself. The non-linearity seems to be weak in our study so the delay in the wave propagation before and after the collision is small. Time-space plots show localized propagating waves with high amplitudes for frequencies near resonance. Between the peaks low amplitude and harmonic patterns are observed. However, for higher frequencies, the frequency band for localized waves becomes wider. In the Fourier space-time plane, this can be observed as a point for the harmonic patterns or a superposition of two lines: one line parallel to wave-vector k axis corresponding to the excitation frequency f_0 and a second line with inclination given by wave propagation velocity sqrt{gh}. For planned future work, this result will help us to reconstruct the whole water surface elevation using time-series from only a few measurement points

A note on rank one quadratic twists of elliptic curves and the non-degeneracy of 𝑝-adic regulators at Eisenstein primes

We show that for certain non-CM elliptic curves E / Q E_{/\mathbb {Q}} such that 3 3 is an Eisenstein prime of good reduction, a positive proportion of the quadratic twists E ψ E_{\psi } of E E have Mordell–Weil rank one and the 3 3 -adic height pairing on E ψ ( Q ) E_{\psi }(\mathbb {Q}) is non-degenerate. We also show similar but weaker results for other Eisenstein primes. The method of proof also yields examples of middle codimensional algebraic cycles over number fields of arbitrarily large dimension (generalized Heegner cycles) that have non-zero p p -adic height. It is not known – though expected – that the archimedian height of these higher-codimensional cycles is non-zero.

Dynamical thin disks

Thin disk accretion is often modeled in highly dynamical settings using the two-dimensional equations of viscous hydrodynamics, with viscosity representing unresolved turbulence. These equations are supposed to arise after vertical integration of the full three-dimensional equations of hydrodynamics, under the assumption of a geometrically thin disk with mirror symmetry about the midplane. However, in the dynamical context, vertical dynamics are neglected by incorrectly assuming instantaneous vertical hydrostatic equilibrium. The resulting errors in the local disk height couple to the horizontal dynamics through the $\ensuremath{\alpha}$-viscosity prescription and disk height-dependent gravitational softening models. Furthermore, the viscous terms in the horizontal equations are only complete if they are inserted after vertical integration, as if the system is actually two-dimensional. Since turbulence breaks mirror symmetry, it is more physically correct to insert a turbulence model at the three-dimensional level and impose mirror symmetry only on average. Thus, some viscous terms are usually missing. With these considerations in mind, we revisit the vertical integration procedure, restricting ourselves to the regime of a Newtonian, non-self-gravitating disk. We obtain six evolution equations with only horizontal dependence, which determine the local vertical position and velocity of the disk surface, in addition to the usual surface densities of mass, horizontal momentum, and energy. This ``2.5-dimensional'' formulation opens the door to efficiently study vertical oscillations of thin disks in dynamical settings, and to improve the treatment of unresolved turbulence. As a demonstration, by including viscous stress at the three-dimensional level, we recover missing viscous terms which involve the vertical variables. We also propose a resummation of the vertically integrated gravitational force, which has a strikingly similar radial profile to a gravitational softening model advocated for in protoplanetary disk studies.

Height pairings of 1-motives

The purpose of this work is to generalize, in the context of 1-motives, the p -adic height pairings constructed by B. Mazur and J. Tate on abelian varieties. Following their approach, we define a global pairing between the rational points of a 1-motive and its dual. We also provide a local pairing between disjoint zero-cycles of degree zero on a curve, which is done by considering the Picard and Albanese 1-motives associated to the curve.

Vortex streets to the lee of Madeira in a kilometre-resolution regional climate model

Abstract. Atmospheric vortex streets are a widely studied dynamical effect of isolated mountainous islands. Observational evidence comes from case studies and satellite imagery, but the climatology and annual cycle of vortex shedding are often poorly understood. Using the non-hydrostatic limited-area COSMO model driven by the ERA-Interim reanalysis, we conducted a 10-year-long simulation over a mesoscale domain covering the Madeira and Canary archipelagos at high spatial (grid spacing of 1 km) and temporal resolutions. Basic properties of vortex streets were analysed and validated through a 6 d long case study in the lee of Madeira Island. The simulation compares well with satellite and aerial observations and with existing literature on idealised simulations. Our results show a strong dependency of vortex shedding on local and synoptic-flow conditions, which are to a large extent governed by the location, shape and strength of the Azores high. As part of the case study, we developed a vortex identification algorithm. The algorithm is based on a set of criteria and enabled us to develop a climatology of vortex shedding from Madeira Island for the 10-year simulation period. The analysis shows a pronounced annual cycle with an increasing vortex-shedding rate from April to August and a sudden decrease in September. This cycle is consistent with mesoscale wind conditions and local inversion height patterns.

Remarks on algebraic dynamics in positive characteristic

AbstractIn this paper, we study arithmetic dynamics in arbitrary characteristic, in particular in positive characteristic. Applying the arithmetic degree and canonical height in positive characteristic, we prove the Dynamical Mordell–Lang Conjecture for automorphisms of projective surfaces of positive entropy, the Zariski Dense Orbit Conjecture for automorphisms of projective surfaces and for endomorphisms of projective varieties with large first dynamical degree. We also study ergodic theory for constructible topology. For example, we prove the equidistribution of backward orbits for finite flat endomorphisms with large topological degree. As applications, we give a simple proof for weak dynamical Mordell–Lang and prove a counting result for backward orbits without multiplicities. This gives some applications for equidistributions on Berkovich spaces.

Quantifying and analysing rock trait distributions of rocky fault scarps using deep learning

AbstractWe apply a deep learning model to segment and identify rock characteristics based on a Structure‐from‐Motion orthomap and digital elevation model of a rocky fault scarp in the Volcanic Tablelands, Eastern California, USA. By post‐processing the deep learning results, we build a semantic rock map and analyse the rock trait distributions. The resulting semantic map contains nearly 230 000 rocks with effective diameters ranging from 2 to 250 cm. Rock trait distributions provide a new perspective on rocky fault scarp development and extend past research on scarp geometry including slope, height and length. Heatmaps indicate rock size spatial distributions on the fault scarp and surrounding topographic flats. Median grain size changes perpendicular to the fault scarp trace, with the largest rocks on the downslope proximal to the scarp footwall. Correlation analyses illustrate the relationship between rock trait statistics and fault scarp geomorphology. Local fault scarp height correlates with median grain size ( = 0.6), the mean grain size of the largest rocks ( = 0.8) and the ratio of the number of small to large rocks ( = 0.4). The positive correlation ( = 0.8) between local fault scarp height and standard deviation of grain size suggests that rocks on a higher fault scarp are less well sorted. The correlation analysis between fault scarp height and rock orientation statistics supports a particle transportation model in which locally higher fault scarps have relatively more rocks with long axes parallel to fault scarp trace because rocks have a larger distance to roll and orient the long axes. Our work demonstrates a data‐driven approach to geomorphology based on rock trait distributions, promising a greater understanding of fault scarp formation and tectonic activity, as well as many other applications for which granulometry is an indicator of process.

Is the anterior cervical dynamic plate fixation better than the anterior static plate fixation: a retrospective review with over 5 years follow-up

BackgroundTo compare the clinical and radiologic outcomes after anterior cervical dynamic or static plate fixation for short segment cervical degenerative disc diseases (DDD) for more than 5 years.MethodsSixty-four patients who underwent anterior cervical one level discectomy or corpectomy with an anterior cervical plate system were followed for an average of 6.8 years for clinical and radiographic outcomes. Among the sixty-four patients, thirty-eight patients were fixed with a static plate (ORION and CSLP plate system) and the other twenty-six patients were fixed with a dynamic plate (ABC plate). Radiographic data were collected included the global sagittal alignment of the cervical spine (C2–C7), the local height and angle of the operated level pre-operatively, postoperatively and at last follow-up. A clinical assessment was performed at pre-operatively, three months postoperatively and final follow-up using the Japanese Orthopedic Association (JOA) /Visual Analogue Score(VAS)/ Neck Disablility Index(NDI) scoring system.ResultsThe mean follow-up time was 6.8 years. At final review, there were two cases of suspicious pseudarthrosis which were from ABC plate fixation group while the other cases all gained solid fusion. The height of fusion segment gained significantly improvement for both dynamic and static plate group post-operation, and all groups demonstrated a significant loss in height postoperatively. Generally, for the one level ACDF group, the height decrease was 0.5 mm for static plate and 1.6 mm for dynamic group which was significantly different(p < 0.05). And for one level ACCF group, this type of difference was not seen in which decreasing was 1.7 mm for static group and 1.8 mm for dynamic group. Segmental lordosis of the fusion segments was increased significantly both post-operation and final follow-up than before-operation for both one and two segments fusion. Global cervical lordosis from C2–C7 was increased in the early postoperative period in all groups, and at final follow-up the total lordosis was still getting better compared with early postoperative period, but this increase was not statistically significant. Clinical assessment of JOA/NDI showed that there was significantly improvement 3-month post-operation compared with pre-operation, and the score could get a slight further improvement at the final follow-up.ConclusionOur study demonstrated a statistically similar fusion rate between dynamic and static cervical plate fixation. However, the height gained with static plate fixation for single segment disease was maintained better than with dynamic plate fixation and there was no difference between JOA outcome scores between groups. Despite the reported improved biomechanics of dynamic plate fixation, further research needs to be done to show the clinical advantage of dynamic plate fixation.

Gradual versus episodic lateral saltmarsh cliff erosion: Evidence from Terrestrial Laser Scans (TLS) and Surface Elevation Dynamics (SED) sensors

As lateral erosion can threaten valuable saltmarsh habitats and their capacity to protect the hinterland from waves and floods, there is a need to understand the mechanisms of erosion. We monitored lateral saltmarsh erosion at high spatiotemporal resolution during a 2.5 year period. We performed terrestrial laser scans (TLS) with centimetric spatial resolution, ca monthly, as well as before and after 2 wind events to assess morphological change of a saltmarsh cliff (<0.8 m in height), and deployed surface elevation dynamics (SED) sensors at 3 locations to obtain daily measurements of the cliff edge position with 2 mm resolution. This was complemented by wind data, and a pressure transducer on the mudflat to obtain time-series of local inundation duration, water depth, wave height, period, power and energy. TLS shows gradual lateral erosion of the marsh edge and surface, and occasional local slumping, with substantial local variation. SED sensor data also reveal that lateral erosion was mostly continuous, with episodes with stronger and weaker local erosion, at all 3 locations, often correlated in space. Correlations between changes in total marsh area and sediment volume of the mudflat-saltmarsh interface from TLS with particularly inundation duration and wind velocity were discussed. At plot level, correlations were not consistent; correlations between the local lateral erosion rates and hydrodynamics/winds were not significant. Results emphasize the importance of common low magnitude events for long-term lateral erosion.