Variable Topography Research Articles

FadeNet: Deep Learning-Based mm-Wave Large-Scale Channel Fading Prediction and its Applications

Accurate prediction of the large-scale channel fading is fundamental to planning and optimization in 5G millimeter-wave cellular networks. The current prediction methods, which are either too computationally expensive or inaccurate, are unsuitable for city-scale cell planning and optimization. This paper presents FadeNet, a convolutional neural-network enabled alternative for predicting large-scale fading with high computation speed and accuracy. By using carefully designed input features and neural-network architecture to capture topographical information, FadeNet accurately predicts the large-scale fading from a base station to each location in its coverage area. Evaluations on realistic data, derived from millimeter-wave cells across multiple cities, suggest that FadeNet can achieve a prediction accuracy of 5.6 decibels in root mean square error. In addition, by leveraging the parallel processing capabilities of a graphics processing unit, FadeNet can reduce the prediction time by $40X-1000X$ in comparison to industry prevalent methods like ray-tracing. Generalizations of FadeNet, that can handle variable topographies and base station heights, and its use for optimal cell site selection are also explored.

Exhumation of the southern transpressive Bucaramanga fault, eastern Cordillera of Colombia: Insights from detrital, quantitative thermochronology and geomorphology

New detrital apatite and zircon fission-track thermochronology ages were determined in four rivers (Onzaga, Los Micos, Mogoticos, and Chaguacá) located along the southern termination of the Bucaramanga Fault System in the Eastern Cordillera of Colombia. Younger populations of apatite fission-track (AFT) ages were found in the Onzaga and Los Micos rivers, both draining the central zone of a transpressive system. The detrital thermochronological data are used to estimate erosion rates, assuming topographic steady-state and spatially variable conditions. We also tested the link between long-to short-term erosion patterns employing Hotspot and Cluster Analysis (HCA) of Hack's stream length index (SL), which enables us to detect transient signals related to landsliding, lithologic variability, or tectonic processes. Based on this classification, we identified 175 SL-HCA anomalies distributed across the study area but mainly concentrated on the western side of the Chicamocha River where gigantic landslides are present. This topographic analysis reveals knickzones where higher erosion rates are expected. Consequently, those hotspots are the source of much of the sediment being evacuated through the Chicamocha River system. This favours the hypothesis that the area has spatially variable topographic conditions over time. To test this, we compare observed and predicted detrital age distributions derived from 3D thermal-kinematic inversions of existing in-situ thermochronological data assuming the two different topography conditions. We show that exhumation rates calculated with the bootstrapping method are closer to the predictions obtained from our 3D thermal-kinematic models with a spatially variable topography assumption. Furthermore, for the Onzaga River, the comparison of cumulative density functions between observed and predicted ages are statistically similar, which validates our hypothesis. Our results demonstrate that the topography has been variable over time, mainly from 40 Ma to the present. Exhumation rates in the study area evolved from ~2 km/m.y. between ~40 and 30 Ma, decreasing to values below 0.1 km/m.y. from 30 to 25 Ma, before increasing to 0.5 km/m.y. from ~20 Ma to the present. The results also indicate that a paleotopography representing 10 to 50% of the current topography was present from 80 to 40 Ma. During the interval between 40 Ma to the present, the model suggests that more than 50% of the present-day topography was created.

Terra: sistema para proyectos de nivelación de tierras con topografía regular o variable

La nivelación de tierras es indispensable para reducir el volumen de agua aplicado y aumentar la uniformidad del riego por gravedad. Se presenta el sistema de cómputo electrónico Terra, para el cálculo de proyectos de nivelación de terrenos agrícolas, útil para examinar innumerables alternativas de diseño en un lapso muy corto de tiempo. Los datos de campo con que se alimenta, pueden ser puntos obtenidos con un levantamiento topográfico de una cuadrícula rectangular o de un levantamiento de distribución variable (radiaciones). El cálculo de volúmenes de corte y relleno se realiza usando ‘el método de los cuatro puntos’ apoyado con el método de Kriging en el caso de la topografía de distribución variable. El algoritmo desarrollado es capaz de dividir el terreno en tablas para su nivelación independiente, con el objetivo de reducir volúmenes de corte y relleno impactando directamente en el costo de nivelación. Se generan planos de la topografía del terreno antes y después de la nivelación; además de planos de cortes y rellenos y un diagrama de bloques como guía para el tractorista en el proceso de nivelación.

Resonant coupling of mode-1 and mode-2 internal waves by topography

Abstract

A Mathematical Model of Stratified Geophysical Fluid Flows Over Variable Bottom Topography

In this paper, a mathematical model of stratified geophysical fluid flow over variable bottom topography was derived for shallow water. The equations are derived from the principles of conservation of mass and conservation of momentum. The force acting on the fluid is gravity, represented by the gravitational constant. A system of six nonlinear partial differential equations was obtained as the model equations. The solutions of these models were obtained using perturbation method. The presence of the coriolis force in the shallow water equations were shown as the causes of the deflection of fluid parcels in the direction of wave motion and causes gravity waves to disperse. As water depth decreases due to varied bottom topography, the wave amplitude were shown to increase while the wavelength and wave speed decreases resulting in overturning of the wave. The results are presented graphically.

Linkage of fine and coarse litter traits to soil microbial characteristics and nitrogen mineralization across topographic positions in a temperate natural forest

Topographic positions within a natural forest can considerably influence litter traits, soil microbial characteristics, and nitrogen (N) mineralization, causing plant–soil feedbacks. Despite the high abundance of coarse litter (woody debris and coarse roots) in forest ecosystems, most studies have focused on linkages between fine litter (leaves and fine roots) and N dynamics and/or the soil microbial community. We investigated the association of fine and coarse litter with soil microbial biomass, community structure, and N mineralization at upper and lower slope positions on sedimentary rocks in a temperate forest dominated by Fagus crenata. Greater coarse litter abundance and litter C-to-N ratio, and lower soil microbial biomass, bacterial abundance, and N mineralization potential were found in upper positions than in lower positions. Among litter traits, coarse litter abundance and litter C-to-N ratio were the best predictors of the microbial biomass and fungal-to-bacterial dominance, possibly due to differences in climatic stress among plant communities. Microbial traits were the best predictors of N mineralization potential. Fine litter traits and coarse litter abundance are likely linked to soil microbial characteristics and N mineralization in natural forests with variable topography.

A Pleistocene deposit preserved in deep karst at Coolough, County Galway, western Ireland

Buried karst features result from a complex interplay between carbonate bedrock and structural geology. The enhancement of carbonate aquifers through this interplay creates hydrogeologically complex subsurface drainage networks and highly variable surface topographies. This article reports on the sediment fill and fossil pollen record from a large enclosed negative karst landform at Coolough, near Galway City in the west of Ireland. The landform was discovered during the preliminary site investigation for the proposed N6 Galway City Ring Road. Major joint sets developed in the Carboniferous (Mississippian) Limestone bedrock govern the local hydrogeology and structural evidence suggests that a local fault has controlled the east–west propagation of the deep enclosed depression. Fluvial and lacustrine palaeoenvironments are interpreted from the sediments infilling the enclosed depression, within which three discrete diamicts are identified, potentially representing distinct phases of glaciation. Pollen assemblages, which reflect palaeoenvironments of open woods and grasslands, have been correlated with other deposits in Ireland and Europe and suggest a minimum date of the Early Pleistocene for the oldest of the diamicts, and thus an upper age limit on the development of the karst depression. Fluvial disturbance to the deposit is evident and is likely to be responsible for the chronological discrepancy between the Early Pleistocene and Middle Pleistocene sediments both recorded from the deposit infill. The findings of this multidisciplinary study contribute to an understanding of Quaternary landscape evolution in western Ireland.

Vertical Accuracy of Freely Available Global Digital Elevation Models (ASTER, AW3D30, MERIT, TanDEM-X, SRTM, and NASADEM)

Freely available global digital elevation models (DEMs) are important inputs for many research fields and applications. During the last decade, several global DEMs have been released based on satellite data. ASTER and SRTM are the most widely used DEMs, but the more recently released, AW3D30, TanDEM-X and MERIT, are being increasingly used. Many researchers have studied the quality of these DEM products in recent years. However, there has been no comprehensive and systematic evaluation of their quality over areas with variable topography and land cover conditions. To provide this comparison, we examined the accuracy of six freely available global DEMs (ASTER, AW3D30, MERIT, TanDEM-X, SRTM, and NASADEM) in four geographic regions with different topographic and land use conditions. We used local high-precision elevation models (Light Detection and Ranging (LiDAR), Pleiades-1A) as reference models and all global models were resampled to reference model resolution (1m). In total, 608 million 1x1 m pixels were analyzed. To estimate the accuracy, we generated error rasters by subtracting each reference model from the corresponding global DEM and calculated descriptive statistics for this difference (e.g., median, mean, root-mean-square error (RMSE)). We also assessed the vertical accuracy as a function of the slope, slope aspect, and land cover. We found that slope had the strongest effect on DEM accuracy, with no relationship for slope aspect. The AW3D30 was the most robust and had the most stable performance in most of the tests and is therefore the best choice for an analysis of multiple geographic regions. SRTM and NASADEM also performed well where available, whereas NASADEM, as a successor of SRTM, showed only slight improvement in comparison to SRTM. MERIT and TanDEM-X also performed well despite their lower spatial resolution.

Cross-Shelf Transport Through the Interaction among a Coastal Jet, a Topographic Wave, and Tides

Shelf break flows are often characterized by along-isobath jets with cross-shelf currents associated with tides and waves guided by variable topography. Here, we address the question: Can a superposition of such flows produce significant aperiodic cross-shelf transport? To answer this question, we use a barotropic analytic model for the jet based on a similarity solution of the shallow water equations over variable topography, a wave disturbance determined by the topography, and a diurnal tidal disturbance. We use standard Lagrangian methods to assess the cross-shelf transport, presenting the results, however, in a Eulerian frame, so as to be amenable to oceanographic observations. The relative roles of the different flow components in cross-shelf transport are assessed through an extensive parameter study. We find that a superposition of all three flow components can indeed produce consequential background aperiodic transport. An application of the model using recent observations from the Texas Shelf demonstrates that a combination of these background mechanisms can produce significant transport under realistic conditions.

Exploring a Convection–Diffusion–Reaction Model of the Propagation of Forest Fires: Computation of Risk Maps for Heterogeneous Environments

The propagation of a forest fire can be described by a convection–diffusion–reaction problem in two spatial dimensions, where the unknowns are the local temperature and the portion of fuel consumed as functions of spatial position and time. This model can be solved numerically in an efficient way by a linearly implicit–explicit (IMEX) method to discretize the convection and nonlinear diffusion terms combined with a Strang-type operator splitting to handle the reaction term. This method is applied to several variants of the model with variable, nonlinear diffusion functions, where it turns out that increasing diffusivity (with respect to a given base case) significantly enlarges the portion of fuel burnt within a given time while choosing an equivalent constant diffusivity or a degenerate one produces comparable results for that quantity. In addition, the effect of spatial heterogeneity as described by a variable topography is studied. The variability of topography influences the local velocity and direction of wind. It is demonstrated how this variability affects the direction and speed of propagation of the wildfire and the location and size of the area of fuel consumed. The possibility to solve the base model efficiently is utilized for the computation of so-called risk maps. Here the risk associated with a given position in a sub-area of the computational domain is quantified by the rapidity of consumption of a given amount of fuel by a fire starting in that position. As a result, we obtain that, in comparison with the planar case and under the same wind conditions, the model predicts a higher risk for those areas where both the variability of topography (as expressed by the gradient of its height function) and the wind velocity are influential. In general, numerical simulations show that in all cases the risk map with for a non-planar topography includes areas with a reduced risk as well as such with an enhanced risk as compared to the planar case.

The Propagation of Nonlinear Internal Waves under the Influence of Variable Topography and Earth’s Rotation in a Two-Layer Fluid

A nonlinear equation of the Korteweg–de Vries equation usually describes internal solitary waves in the coastal ocean that lead to an exact solitary wave solution. However, in any real application, there exists the Earth’s rotation. Thus, an additional term is required, and consequently, the Ostrovsky equation is developed. This additional term is believed to destroy the solitary wave solution and form a nonlinear envelope wave packet instead. In addition, an internal solitary wave is commonly disseminated over the variable topography in the ocean. Because of these effects, the Ostrovsky equation is retrieved by a variable-coefficient Ostrovsky equation. In this study, the combined effects of both background rotation and variable topography on a solitary wave in a two-layer fluid is studied since internal waves typically happen here. A numerical simulation for the variable-coefficient Ostrovsky equation with a variable topography is presented. Two basic examples of the depth profile are considered in detail and sustained by numerical results. The first one is the constant-slope bottom, and the second one is the specific bottom profile following the previous studies. These indicate that the combination of variable topography and rotation induces a secondary trailing wave packet.

A new form of the Saint-Venant equations for variable topography

Abstract. The solution stability of river models using the one-dimensional (1D) Saint-Venant equations can be easily undermined when source terms in the discrete equations do not satisfy the Lipschitz smoothness condition for partial differential equations. Although instability issues have been previously noted, they are typically treated as model implementation issues rather than as underlying problems associated with the form of the governing equations. This study proposes a new reference slope form of the Saint-Venant equations to ensure smooth slope source terms and eliminate one source of potential numerical oscillations. It is shown that a simple algebraic transformation of channel geometry provides a smooth reference slope while preserving the correct cross-section flow area and the total Piezometric pressure gradient that drives the flow. The reference slope method ensures the slope source term in the governing equations is Lipschitz continuous while maintaining all the underlying complexity of the real-world geometry. The validity of the mathematical concept is demonstrated with the open-source Simulation Program for River Networks (SPRNT) model in a series of artificial test cases and a simulation of a small urban creek. Validation comparisons are made with analytical solutions and the Hydrologic Engineering Center's River Analysis System (HEC-RAS) model. The new method reduces numerical oscillations and instabilities without requiring ad hoc smoothing algorithms.

Fission law of solitary waves propagating over sharply variable topography

The fission of solitary waves propagating over variable topography is investigated. In previous theories, to predict the number and the amplitudes of disintegrated solitons in the wave packet generated from a solitary wave, the parameters of the water environment and the incident solitary wave are required. However, it is difficult to measure these parameters in the ocean because of their temporal and spatial variations. In this paper, a fission law, in the form of the expressions of the number and the amplitudes of the disintegrated solitons, is derived from the partial information available on the wave packet. Theoretical analysis shows that the law is suitable for describing the fission of both surface and internal solitary waves and is also applicable to the cases of wave damping and wave breaking. Comparisons between the model output and the results from laboratory experiments, numerical simulations and field observations available in the literature demonstrate that the fission law can efficiently estimate the number and the amplitudes of solitons in the wave packet generated by a solitary wave.

Mathematical Model of Geophysical Fluid Flow over Variable Bottom Topography

In this paper, the bottom topography of a geophysical fluid flow is modelled in the presence of Coriolis force by the nonlinear shallow water equations. These equations, which are a system of three partial differential equations in two space dimensions, are solved using the perturbation method. The Effects of the Coriolis force and the bottom topography for particular initial flows on the velocity components and different kind of flow patterns possible in geophysical fluid flow have been studied and the results illustrated graphically.

Meteorological trends over Satluj River Basin in Indian Himalaya under climate change scenarios

Temperature and precipitation distributions depend on variable topography and heterogeneous landuse/landcover in the Indian Himalayan Region (IHR). It imparts a major concern for hydrological, glaciological modelling, dam structure assessment, etc. Thus, there is an inherent requirement of robust information for climate impact studies over the topographical variable and landuse heterogenous region in the Indian Himalayan Region (IHR). In particular, the importance of bias corrections become critically important over Himalayan river basins, in which model outputs with the corresponding in-situ observations are used for improving the model distribution. These improved details in present and future, as well, are important to carry out the climate change impact studies at basin scale for hydrological, glaciological, climatological studies, etc. Thus, in the present study firstly, model fields are bias corrected with the corresponding in-situ observations. And then trends in these bias corrected data is compared with the corresponding in-situ observations. These assessment of present and future changes in temperature and precipitation over Satluj River Basin (SRB) located in the western Himalayas is illustrated. Model fields are considered from a Regional climate model (REMO) from Coordinated Regional Downscaling Experiment-South Asia (CORDEX-SA) in three Representative Concentration Pathways (RCPs), i.e., 2.6, 4.5 and 8.5 W/m2. These projections are bias corrected using distributed quantile mapping. The precipitation (temperature) bias correction is performed using the distributed quantile mapping on the gamma (normal) distribution. The standard trend statistics is applied for quantitative assessment. A good capture of bias correction in temperature and precipitation is illustrated. Efficient bias removal is depicted in cumulative distribution curve (CDF) at individual station. Trend analysis shows that highest rate of precipitation decrement at low altitude station (Kasol) with the rate of −6.362 mm/year in RCP 8.5. Over the SRB highest rate of temperature increment is seen at highest altitude station (Kaza) with the rate of 0.084°C/year in RCP 8.5. On an average, fall in precipitation and increase in temperature with >99% confidence level in RCP 8.5 is seen. In addition, intensity lowers in other lower RCPs. The study sums up with the efficacy of CORDEX-SA REMO model in capturing present and future change in temperature and precipitation over the SRB in western Himalayas using the bias correction.

The spatial extent and timescales of bank infiltration and return flows in an upland river system: Implications for water quality and volumes

The temporary storage of river water in riverbanks and its subsequent return to the river is an important part of the hydrological cycle. Detailed multi-year head and electrical conductivity (EC) variations document the spatial and temporal scales of bank infiltration and return flows in the Ovens catchment, southeast Australia. The study represents one of only a few that has integrated geochemical data and hydraulic heads over several hydrological cycles in a catchment unimpacted by groundwater extraction. The river water infiltrates only a few metres to tens-of-metres into the riverbanks and dilution of regional groundwater in the banks is commonly observed for several weeks to months following high river stages. Two-dimensional numerical modelling shows that the extent and timescales of bank infiltration and return flows are governed mainly by the regional head gradients, hydraulic conductivities, and the height of the stream pulse. Variable topography in river catchments will result in significant variations in the volumes of bank storage and the timescales that these bank waters are retained. The combination of field observations and numerical modelling illustrates that parts of the riverbanks may store water for several months to years and reconnection of rivers to the regional groundwater will occur in different parts of the catchment at different times. In much of the catchment the bank storage zones act as a buffer against contaminated regional groundwater and bank return flows will sustain streamflow and riverine ecosystems during dry periods.

Monitoring Geomorphic and Traditional Post-Mine Reclamation using Digital Imagery: Vegetative Heterogeneity and Sampling Efficiency

Geomorphic reclamation creates variable topography and surface architecture, including rolling hillslopes and drainages. In contrast, traditional methods of reclamation result in landscapes susceptible to erosion due to steep, linear gradients. Geomorphic approaches to surface mine reclamation are relatively new, and hypotheses suggest the use of geomorphic principles in reclamation will improve vegetation outcomes relative to traditional methods. Topographic variability created by geomorphic reclamation likely results in more environmental heterogeneity, which should correlate with greater plant diversity. We examined revegetation outcomes of traditional and geomorphic reclamation on two reclaimed surface mines in Wyoming using nadir image sampling. Functional group diversity and measures of cover were compared between reclamation methods and undisturbed rangeland. Geomorphic reclamation supported greater total richness and greater native functional group richness relative to traditional reclamation. Native species cover on geomorphic reclamation, particularly for native perennial grasses, was either similar to undisturbed rangeland or greater than undisturbed rangeland and traditional reclamation. Reclamation shrub cover differed significantly from undisturbed sites, but was greater in geomorphic treatments. Results of nadir image analysis are compared to line-point intercept data from the same locations and outcomes are discussed in light of different reclamation techniques and sampling methods. Significant differences in cover categories were observed between nadir image and line-point intercept methods, however both methods revealed similar patterns between study sites.

Zeroth‐order conservation laws of two‐dimensional shallow water equations with variable bottom topography

AbstractWe classify zeroth‐order conservation laws of systems from the class of two‐dimensional shallow water equations with variable bottom topography using an optimized version of the method of furcate splitting. The classification is carried out up to equivalence generated by the equivalence group of this class. We find additional point equivalences between some of the listed cases of extensions of the space of zeroth‐order conservation laws, which are inequivalent up to transformations from the equivalence group. Hamiltonian structures of systems of shallow water equations are used for relating the classification of zeroth‐order conservation laws of these systems to the classification of their Lie symmetries. We also construct generating sets of such conservation laws under action of Lie symmetries.

The variance of clavicular surface morphology is predictable: an analysis of dependent and independent metadata variables

BackgroundThe anatomy of the clavicle is specific and varied in reference to its topography and shape. These anatomic characteristics play an important role in the open treatment of clavicle fractures. The complex and variable topography creates challenges for implant placement, contouring, and position. Hardware prominence and irritation does influence the decision for secondary surgical intervention.MethodsComputerized tomographic scans of 350 adult clavicles with the corresponding patients' metadata were acquired and digitized. Morphologic parameters determining the shape of the clavicle were defined and computed for each digitized bone. The extracted morphologic parameters were correlated with patient metadata to analyze the relationship between morphologic variability and patient characteristics.ResultsThe morphologic parameters defining the shape, that is, the radius of the medial and lateral curves, the apparent clavicle height and width, and the clavicle bow position, correlate with the clavicle length. The clavicle length correlates with the patients' height. Gender differences in shape and form were dependent and related to individual height distribution and clavicle length. Asian populations showed a similarly predictable, but shifted, correlation between shape and clavicle length.ConclusionThis anatomic analysis shows that the clavicle shape can be predicted through the clavicle length and patients' stature. Smaller patients have shorter and more curved clavicles, whereas taller patients have longer and less curved clavicles. This correlation will aid surgeons in fracture reduction, implant curvature selection, and in optimal adaptation of clavicle implants, and represents the basis for anatomically accurate solutions for clavicle osteosynthesis.

Boussinesq-Peregrine water wave models and their numerical approximation

In this paper we consider the numerical solution of Boussinesq-Peregrine type systems by the application of the Galerkin finite element method. The structure of the Boussinesq systems is explained and certain alternative nonlinear and dispersive terms are compared. A detailed study of the convergence properties of the standard Galerkin method, using various finite element spaces on unstructured triangular grids, is presented. Along with the study of the Peregrine system, a new Boussinesq system of BBM-BBM type is derived. The new system has the same structure in its momentum equation but differs slightly in the mass conservation equation compared to the Peregrine system. Further, the finite element method applied to the new system has better convergence properties, when used for its numerical approximation. Due to the lack of analytical formulas for solitary wave solutions for the systems under consideration, a Galerkin finite element method combined with the Petviashvili iteration is proposed for the numerical generation of accurate approximations of line solitary waves. Various numerical experiments related to the propagation of solitary and periodic waves over variable bottom topography and their interaction with the boundaries of the domains are presented. We conclude that both systems have similar accuracy when approximate long waves of small amplitude while the Galerkin finite element method is more efficient when applied to BBM-BBM type systems.