Variable Topography Research Articles

A new well-balanced spectral volume method for solving shallow water equations over variable bed topography with wetting and drying

A new well-balanced spectral volume method for solving shallow water equations over variable bed topography with wetting and drying

A Predictor–corrector scheme for simulation of two-phase granular flows over a moved bed with a variable topography

In this paper, we propose a numerical simulation of two-phase shallow granular flows through a moved bed with a variable irregular topography via a predictor corrector scheme. This method consists of predictor and corrector stages. The predictor stage contains a parameter to control the numerical diffusion that is performed by utilizing limiters and Riemann invariant theory. The corrector stage recovers the balance conservation equation. In the first part, we solve numerically the one-dimensional equation for two-phase shallow granular flows over a fixed bed with irregular topography. In the second part, we consider the model equations for the bed-load sediment transport, the governing model equations consist of two components, specifically, a geophysical flows part and interstitial fluid. The sediment part is described by the Exner equation when the velocity can be considered to be the solid velocity, fluid velocity or a mean value of both of them.

Numerical algorithms for water waves with background flow over obstacles and topography

We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in two dimensions with background flow over a periodic, multiply connected fluid domain that includes stationary obstacles and variable bottom topography. One approach is formulated in terms of the surface velocity potential while the other evolves the vortex sheet strength. Both methods employ layer potentials in the form of periodized Cauchy integrals to compute the normal velocity of the free surface, are compatible with arbitrary parameterizations of the free surface and boundaries, and allow for circulation around each obstacle, which leads to multiple-valued velocity potentials but single-valued stream functions. We prove that the resulting second-kind Fredholm integral equations are invertible, possibly after a physically motivated finite-rank correction. In an angle-arclength setting, we show how to avoid curve reconstruction errors that are incompatible with spatial periodicity. We use the proposed methods to study gravity-capillary waves generated by flow around several elliptical obstacles above a flat or variable bottom boundary. In each case, the free surface eventually self-intersects in a splash singularity or collides with a boundary. We also show how to evaluate the velocity and pressure with spectral accuracy throughout the fluid, including near the free surface and solid boundaries. To assess the accuracy of the time evolution, we monitor energy conservation and the decay of Fourier modes and compare the numerical results of the two methods to each other. We implement several solvers for the discretized linear systems and compare their performance. The fastest approach employs a graphics processing unit (GPU) to construct the matrices and carry out iterations of the generalized minimal residual method (GMRES).

Spatial and temporal simulation of groundwater recharge and cross-validation with point estimations in volcanic aquifers with variable topography

Study regionThis study is performed for the volcanic aquifers of semi-humid Lake Tana basin in northwest Ethiopia, the source region of Blue Nile basin. Study focusestimating groundwater recharge at required spatial and temporal scale is a challenge in groundwater management, sustainability and pollution studies. In this study, the physically-based WetSpass model is applied. The recharge by WetSpass is validated with estimations by water table fluctuation (WTF) and chloride mass balance (CMB) methods. Evaluating the groundwater recharge estimation mechanism for the volcanic aquifers lying at different topographical setting, that represents wide part of the world groundwater aquifers, and suggesting more appropriate methods will benefit different similar studies. New hydrological insights for the regionthe mean annual rainfall, recharge, surface runoff, and evapotranspiration are estimated at 1431 mm, 315 mm, 416 mm, and 770 mm, respectively. The recharge varies from 0% to 57% of the rainfall. A high variation is also noted using WTF and CMB methods showing the strong heterogeneous nature of the hydro(meteoro)logical characteristics of the area. WetSpass is effective in aquifers where diffuse recharging mechanism is the predominant type and recharge is controlled by rainfall. Hence, it is found less effective in the storage-controlled flat floodplain, alluvial and fractured rock aquifer areas. In these areas, the point estimates by the WTF and CMB are effective and can be considered as reliable values.

Self-adaptability and topological deformation of Ganlan architectural heritage: Conservation and regeneration of Lianghekou Tujia village in Western Hubei, China

The authenticity of architectural heritage is interpreted differently in diverse cultural traditions. Can this inspire the conservation and contemporary regeneration of architectural heritage to adapt to the changing needs of modern life and society, rather than static exhibits in museums? This research focuses on Ganlan (pile-built timber construction) architecture to demonstrate how adaptive conservation and regeneration can keep traditional construction systems living and sustainable. Ganlan, a vernacular architectural archetype in the humid subtropical regions of Asia, has the following common features: free plans with an assembling frame structure, open and interactive envelopes to cope with the hot and damp climate, and stilts to deal with the rugged terrain. This research employed a threefold method of field investigation, topological deformation, and experimental design in examining Lianghekou, a historic Tujia village in Western Hubei, China. The findings reveal that Tujia people build their stilt houses with adaptable features to meet the changing functional requirements and variable topographies. These traditions can be transmitted into the contemporary design, as our experimental design illustrates. The self-adaptability and topological deformation of Ganlan architectural heritage demonstrate a unique perspective of understanding authenticity, and contribute toward innovative application in the conservation and regeneration of vernacular architecture.

Bidirectional Whitham type equations for internal waves with variable topography

In the context of oceanic internal gravity waves, one of the most widely-used theories on examining wave dynamics and interpreting observational data is the Korteweg–de Vries (KdV) equation. Nonetheless, the characters of unidirectional propagation and unbounded phase and group velocities restrict its application to some general cases (Benjamin et al., 1972). Thus, using the Dirichlet–Neumann operator with the rigid-lid approximation, we derive both bidirectional and unidirectional Whitham type equations in the Hamiltonian framework, which retain the full linear dispersion relation of the Euler equations. The effect of topography is also incorporated in modeling due to its practical relevance, although the invoked scaling plausibly excludes the accommodation of a significant bottom variation. There are no analytic solutions of internal solitary waves explicitly given in the newly proposed equations, even though these equations possess a concise form. Therefore, a modified Petviashvili iteration method is implemented to obtain the numerical solutions to circumvent this difficulty. Facilitated by these techniques, several numerical experiments are investigated and compared among different models: the KdV equation, the Whitham type equations, and the primitive equations. The discrepancies and similarities between the various models jointly indicate the advantage of full dispersion and bidirectional propagation and, thus, the effectiveness of the Whitham type equations.

Medium amplitude model for internal waves over large topography variation

The purpose of this paper is to present the derivation and mathematical analysis of a new asymptotic model that describes the evolution of medium amplitude internal waves propagating between a flat rigid-lid and a highly variable topography. The smallness assumptions on the topographic variation parameter used in Lteif et al. (2015) [19] and in Lteif and Israwi (2018) [18] are now relaxed and the results of the aforementioned papers are improved and generalized to the complex case of large topography variation. Limiting the flow to one-layer, we also emphasize our model's well-posedness in comparison to the original asymptotic model.

Effects of mesoscale turbulence on the wind-driven circulation in a closed basin with topography

This paper studies the effects of time-dependent, mesoscale turbulence on the wind-driven ocean circulation in a closed basin with variable topography. Numerical simulations of a single-layer fluid with finite topography at the sloping boundaries are performed. The flow is forced by a suitable combination of a steady, basin-scale wind that generates the classical western-intensified anticyclonic gyre, plus a shorter, time-dependent forcing that injects energy at a narrow range of scales. Two contrasting situations are considered. First, in the absence of the large-scale forcing, the turbulence generates a cyclonic flow that follows the geostrophic contours around the basin. Second, the resulting mean circulation is studied when the large and small-scale forcing terms are considered together. In particular, it is discussed that the alteration of the anticyclonic gyre may be due to the turbulent-induced cyclonic circulation.

Real vehicle fuel consumption in logistic corridors

Fleet managers state that fuel consumption accounts for 50% of the operating costs of their cargo and passenger vehicle fleets. Aiming to reduce these costs, transport companies contract telematics services to track their units and monitor fuel consumption along with other variables. The gathered information is used to alert managers on events like excessive fuel consumption, abrupt breaks, and needs for mechanical maintenance. We propose the use of this information to determine the fuel consumption of cargo vehicles at each km of the main roads of a given region and the influence of altitude, road grade, and vehicle age on it. As a case study, we studied the fuel consumption in the main logistic corridor of Colombia, which is characterized by having a highly variable topography. Toward that end, we compared the fuel consumption monitored by a telematics system on 46 vehicles of different cargo capacity with the estimated by an energy balance model and observed that they are highly correlated (R2 greater than 0.99). Then, we used the calibrated model to obtain the km-by-km fuel consumption. This information is used by authorities to obtain a close estimation of the cost of cargo transport, the greenhouse gases emissions and to identify locations with unusual high fuel consumption. Furthermore, the slope of the linear correlation (Cf) decouples the fuel consumption associated with driving style (human factors) from other influencing factors. Then, we observed that the effects of altitude on fuel consumption are negligible.

An automatically well-balanced formulation of pressure forcing for discontinuous Galerkin methods for the shallow water equations

This paper begins a development of methods for addressing variable bottom topography in discontinuous Galerkin numerical methods for multi-layer, variable-density models of ocean circulation. For numerical models of ocean circulation, it is a widespread practice to split the fast (external) and slow (internal) dynamics into separate subsystems that are solved by different techniques. The fast dynamics are modeled by a vertically-integrated system that is very similar to the shallow water equations for a hydrostatic fluid of constant density. As a first step, the present paper focuses on variable bottom topography for the shallow water equations; extensions to the multi-layer case will be reported elsewhere.A central point of this work, for both the shallow water and the multi-layer cases, is the representation of the pressure forcing in the momentum equations. For the shallow water case, the present work does not use the standard representation of the pressure forcing that is widely used for the shallow water system. Instead, it begins with a more basic form of the momentum equations for a fluid flow, and it proceeds directly to a weak Galerkin form via integration over a suitable fluid region. The resulting formulation of the momentum equations is automatically well-balanced, subject to an assumption that the algorithms used to compute quantities at cell edges reproduce the continuous values in the case where all functions involved are continuous. In addition, this formulation has a structure that is analogous to that of the momentum equations in the individual layers of a multi-layer fluid, and this facilitates consistency between the two subsystems that are used to model such a fluid.The numerical computations described here include tests of well-balancing and tests of wave propagation over variable topography.

Evolution of interface singularities in shallow water equations with variable bottom topography

AbstractWave front propagation with nontrivial bottom topography is studied within the formalism of hyperbolic long wave models. Evolution of nonsmooth initial data is examined, and, in particular, the splitting of singular points and their short time behavior is described. In the opposite limit of longer times, the local analysis of wave fronts is used to estimate the gradient catastrophe formation and how this is influenced by the topography. The limiting cases when the free surface intersects the bottom boundary, belonging to the so‐called “physical” and “nonphysical” vacuum classes, are examined. Solutions expressed by power series in the spatial variable lead to a hierarchy of ordinary differential equations for the time‐dependent series coefficients, which are shown to reveal basic differences between the two vacuum cases: for nonphysical vacuums, the equations of the hierarchy are recursive and linear past the first two pairs, whereas for physical vacuums, the hierarchy is nonrecursive, fully coupled, and nonlinear. The former case may admit solutions that are free of singularities for nonzero time intervals, whereas the latter is shown to develop nonstandard velocity shocks instantaneously. Polynomial bottom topographies simplify the hierarchy, as they contribute only a finite number of inhomogeneous forcing terms to the equations in the recursion relations. However, we show that truncation to finite‐dimensional systems and polynomial solutions is in general only possible for the case of a quadratic bottom profile. In this case, the system's evolution can reduce to, and is completely described by, a low‐dimensional dynamical system for the time‐dependent coefficients. This system encapsulates all the nonlinear properties of the solution for general power series initial data, and, in particular, governs the loss of regularity in finite times at the dry point. For the special case of parabolic bottom topographies, an exact, self‐similar solution class is introduced and studied to illustrate via closed‐form expressions the general results.

Well-balanced numerical resolution of the two-layer shallow water equations under rigid-lid with wet–dry fronts

In this paper, we present a well-balanced numerical scheme for the frictional two-layer shallow water equations (2LSWE) over variable bottom topography and under a rigid-lid (RL) to simulate internal waves propagating over wet and dry areas. Following the idea of Liang and Borthwick (2009) for the derivation of a pre-balanced formulation for one-layer flows, we derive a new formulation of the 2LSWE-RL using the interface elevation above datum and horizontal momentum as conservative variables. This new formulation mathematically balances the flux gradient and source terms so that the lake-at-rest steady state is automatically preserved in wet-bed applications. A proper discretization of the slope source term is adopted to produce well-balanced solutions in dry-bed areas where the lower layer depth vanishes. Using the Harten, Lax, and van Leer (HLL) approximate Riemann solver, we adopt a finite volume MUSCL-RK2 method to construct a second-order well-balanced numerical scheme ensuring the non-negativity of the layers depths with a special treatment of source terms. Finally, various numerical experiments are tested in both one and two-layer cases validating the properties of the numerical scheme.

Landsat Snow-Free Surface Albedo Estimation Over Sloping Terrain: Algorithm Development and Evaluation

Surface albedo plays a key role in global climate modeling as a factor controlling the energy budget. Satellite observations were utilized to estimate surface albedo at global and regional scales with good precision over flat areas. However, because topography greatly complicates radiative transfer (RT) processes, estimating the albedo of rugged terrain with satellite data remains a challenge. In addition, albedo definitions over sloping terrain differ from that for flat areas. They include horizontal/horizontal sloped surface albedo (HHSA) and inclined/inclined sloped surface albedo (IISA). Methods for retrieving HHSA and IISA in mountains have not been well-explored. Here, we retrieved HHSA and IISA on sloping terrain from Landsat 8 using a direct estimation algorithm. We simulated a dataset of Landsat top-of-atmosphere (TOA) reflectance and surface albedo with discrete anisotropic radiative transfer (DART) model, for variable atmospheric, vegetation, soil, and topography properties. Then, we used artificial neural networks (ANNs) to derive an empirical relationship between TOA reflectance and surface albedo. The accuracy of our method was verified with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> measurements: root mean squared error (RMSE) and bias equal to 0.029 and −0.010 for HHSA, and 0.023 and −0.001 for IISA, respectively. Several albedo results (HHSA, IISA, values without topographic consideration) were evaluated and compared. HHSA was found similar to albedo without topographic consideration, but IISA, considered as the “true albedo” for sloping terrain, showed large difference from them. This study demonstrated the feasibility of surface albedo estimation from Landsat TOA reflectance directly in rugged terrains and advanced our understanding of energy budget in mountains.

Microfluidic water flow on laser-patterned MicroCoat® - coated steel surface

A series of hybrid textures with variable topography and chemical composition were obtained on a hydrophilic steel (AISI 304) substrate with a hydrophobic MicroCoat® coating at the increasing incident nanosecond laser fluence from 1.4 J/cm2 to 5.6 J/cm2. The microtopography of the textured surface was studied by laser microscopy and scanning electron microscopy (SEM), while the chemical composition of the surface was determined by IR spectroscopy. The contact angles of water wetting in the textured areas varied versus laser fluence from about 100° to 10°, which was explained by both ablative removal of the hydrophobic polymer coating and the increase in roughness of the hydrophilic steel surface. The time dependence of the contact angle on the different textures, which demonstrated hydrophobization at different time scales depending on the texturing conditions, was analyzed. Autonomous directional flow was observed on laser-patterned wetting-gradient structures of various shapes, and the flow velocity of water droplets on these structures were measured. It was shown that the velocity of water drop spreading on the gradient structures depends on the difference in contact angles on adjacent spots. The various modules fabricated can be harnessed in chemical and biomedical microfluidic devices.

Submerged breakwater of a flexible porous membrane with a vertical flexible porous wall over variable bottom topography

An analytical model of oblique wave interaction with a breakwater consisting of a submerged horizontal flexible porous membrane near a vertical porous barrier over variable bottom topography is developed based on linear water wave theory. Using Green's second identity, a mild-slope equation for oblique waves propagating over a submerged porous membrane and a finite variable bottom topography is derived. The analytical solution of the referred problem is obtained by using the eigenfunction expansion method along with the mild-slope equation and Darcy's law is used for wave past horizontal and vertical porous structure. The present results are compared with existing published analytical results and experimental data and observed that they have a good level of agreement. The effect of different design parameters on the wave quantities and wave forces on the porous wall in variable bottom depth is analyzed. It is found that full-wave reflection is drastically reduced and the wave energy is dissipated by the submerged horizontal flexible porous membrane and porous barrier. The analysis of the reflection and dissipation coefficients as well as wave forces on the vertical wall in terms of wave energy dissipation and wave loads by the proposed submerged flexible porous breakwater will be helpful for better understanding in the design of various types of protecting infrastructures for marine operations.

Lightning-ignited wildfires and long continuing current lightning in the Mediterranean Basin: preferential meteorological conditions

Abstract. Lightning is the major cause of the natural ignition of wildfires worldwide and produces the largest wildfires in some regions. Lightning strokes produce about 5 % of forest fires in the Mediterranean Basin and are one of the most important precursors of the largest forest fires during the summer. Lightning-ignited wildfires produce significant emissions of aerosols, black carbon, and trace gases, such as CO, SO2, CH4, and O3, affecting air quality. Characterization of the meteorological and cloud conditions of lightning-ignited wildfires in the Mediterranean Basin can serve to improve fire forecasting models and to upgrade the implementation of fire emissions in atmospheric models. This study investigates the meteorological and cloud conditions of lightning-ignited wildfires (LIWs) and long continuing current (LCC) lightning flashes in the Iberian Peninsula and Greece. LCC lightning and lightning in dry thunderstorms with a low precipitation rate have been proposed to be the main precursors of the largest wildfires. We use lightning data provided by the World Wide Lightning Location Network (WWLLN), the Earth Networks Total Lightning Network (ENTLN), and the Lightning Imaging Sensor (LIS) on board the International Space Station (ISS), together with four databases of wildfires produced in Spain, Portugal, southern France, and Greece, respectively, in order to produce a climatology of LIWs and LCC lightning over the Mediterranean Basin. In addition, we use meteorological data provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA5 reanalysis data set and by the Spanish State Meteorological Agency (AEMET), together with the Cloud Top Height product (CTHP) derived from Meteosat Second Generation (MSG) satellites measurements to investigate the meteorological conditions of LIWs and LCC lightning. According to our results, LIWs and a significant amount of LCC lightning flashes tend to occur in dry thunderstorms with weak updrafts. Our results suggest that LIWs tend to occur in clouds with a high base and with a vertical content of moisture lower than the climatological value, as well as with a higher temperature and a lower precipitation rate. Meteorological conditions of LIWs from the Iberian Peninsula and Greece are in agreement, although some differences possibly caused by the highly variable topography in Greece and a more humid environment are observed. These results show the possibility of using the typical meteorological and cloud conditions of LCC lightning flashes as proxy to parameterize the ignition of wildfires in atmospheric or forecasting models.

Pterional variable topography and morphology. An anatomical study and its clinical significance

Pterion is the junction of the frontal, parietal, greater wing of the sphenoid and the squamous part of the temporal bone. The sphenoparietal, frontotemporal, stellate and epipteric pteria were described. The current study determines pterion topography, morphology (variant types' frequency) and morphometry, as well as epipteric bones presence in dried skulls. Gender impact is underlined as well. Ninety Greek adult dried skulls were observed. The distances in between pterion and the zygomatic arch midpoint and in between pterion and the frontozygomatic suture were measured. The sphenoparietal pterion was the commonest (58.3%), following by the stellate (25%), epipteric (15.5%) and by the frontotemporal pterion (1.1%). Twenty-eight (15.5%) skulls had epipteric bones, further categorised as quadrisutural (35.7%), trisutural (57.1%), bisutural and multiple (3.57%). The mean distances between pterion and the midpoint of zygomatic arch were 4.13 ± 0.45 cm on the right and 4.09 ± 0.47 cm on the left side and between pterion and the frontozygomatic suture were 3.47 ± 0.61 cm on the right and 3.52 ± 0.65 cm on the left side. Both distances were symmetrical. Male skulls showed slightly higher values on the left side for the distance (pterion-midpoint of zygomatic arch). Pterion is a commonly used neurosurgical landmark and thus in depth knowledge of the pteric area and its variants could be valuable. Recognition of the possible variability in pterion location, morphology and morphometry, as well as possible occurrence of epipteric bones may render pterional craniotomy safer among different population groups.

New Insights Into the Rift to Drift Transition Across the Northeastern Nova Scotian Margin From Wide‐Angle Seismic Waveform Inversion and Reflection Imaging

AbstractSparse wide‐angle seismic profiling supported by coincident reflection imaging has been instrumental for advancing our knowledge about rifted margins. Nevertheless, features of critical importance for understanding rifting processes have been poorly resolved. We derive a high‐resolution velocity model by applying full waveform inversion to the dense OETR‐2009 wide‐angle seismic profile crossing the northeastern Nova Scotian margin. We then create a coincident reflection image by prestack depth migrating the multichannel seismic data. This allows for the first detailed interpretation of the structures related to the final stages of continental breakup and incipient oceanic accretion at the Eastern North America Margin. Our interpretation includes a hyperextended continental domain overlying partially serpentinized mantle, followed by a 10‐km‐wide domain consisting of a continental block surrounded by layered and bright reflectors indicative of magmatic extrusions. A major fault, representing the continent‐ocean boundary, marks a sharp seaward transition to a 16‐km‐wide domain characterized by smoother basement with chaotic reflectors, where no continental materials are present and a 3‐km‐thick embryonic oceanic crust overlying partially serpentinized mantle is created by the breakup magmatism. Further seaward, thin oceanic crust overlies the serpentinized mantle suggesting magma‐poor oceanic spreading with variable magma supply as determined from variable basement topography, 2–4 km thick volcanic layer, and magnetic anomalies. Our results demonstrate that magmatism played an important role in the lithospheric breakup of the area crossed by the OETR‐2009 profile. Considering that the northeastern Nova Scotian margin has been classified as amagmatic, large margin‐parallel variations in magma supply likely characterize a single rift segment.

The Impact of Weather and Slope Conditions on the Productivity, Cost, and GHG Emissions of a Ground-Based Harvesting Operation in Mountain Hardwoods

Mountainous hardwood mixed stands offer challenges to timber harvesting operations in practice, including a harsh climate, variable topography, steep terrain, and large-sized timbers. This paper aims to develop productivity and cost models for a mountain-ground-based harvesting operation across the terrain (e.g., slope conditions), stand (e.g., tree volume) environmental (e.g., weather), and yard (e.g., winching distance) variables and to assess GHG emissions related to the equipment in use. This development was implemented in a timber harvesting practice under single-tree selection in mountainous forests of Iran where a motor-manual chainsaw is used for felling and a rubber-tired cable skidder is used for log extraction. The average delay-free productivity was 4.55 m3 for felling and 14.73 m3 h−1 for skidding. Lower production costs and higher productivity rates were observed over the gentle slopes and in sunny conditions. The average production costs ranged between USD 4.27 m−3 for felling and USD 5.35 m−3 for skidding. The average emissions ranged between 0.96 kg m−3 for felling and 7.06 kg m−3 for skidding in snowy conditions over steep slopes. The study’s results confirm avoiding harvesting operations on steep slopes (greater than 35%) and in extreme weather conditions to obtain higher work efficiency and to minimize adverse effects of machinery on forest ecosystems. The results should be of use to harvest managers and forest planners considering the application of ground-based harvesting operations using a semi-mechanized system on a range of operating conditions in mountain hardwood stands.

State of Crop Landraces in Arcadia (Greece) and In-Situ Conservation Potential

Genetic erosion of landraces is increasing worldwide, however there are still regions rich in landrace biodiversity, such as islands and mountainous isolated areas. Defining the reasons of landrace abandonment in these areas, as well as collecting and preserving landraces, is of outmost importance. In this context, the Agricultural University of Athens organized missions in 53 villages of Arcadia, a prefecture rich in floral biodiversity and variable climatic conditions and topography. The aim was to collect samples of the on-farm (in-situ) conserved annual crop landraces and record the location of perennial crop local varieties. Since traditional knowledge and practices have been playing a vital role in the survival of landraces and local varieties, information was obtained through personal interviews with locals using semi-structured questionnaires. Even though the number of accessions collected from Arcadia has been reduced (141 samples) compared to previous collections and genetic erosion is advancing dramatically for cereals and pulses, a significant number of landraces is still cultivated by the locals. The reasons of landrace abandonment were other sources of occupation than agriculture, such as public service jobs, mechanization, and commercialization of agriculture. Gastronomic and agro-tourism along with European Union trademarks and policies can support locals in landrace/local varieties in-situ conservation.