A High Order Finite Volume Scheme for the 2D Shallow Water Equations Including Topography

Inhalt dieser Arbeit ist ein Verfahren zur numerischen Lösung der zweidimensionalen Flachwassergleichung, welche das Fließverhalten von Gewässern, deren Oberflächenausdehnung wesentlich größer als deren Tiefe ist, modelliert. Diese Gleichung beschreibt die gravitationsbedingte zeitliche Änderung eines gegebenen Anfangszustandes bei Gewässern mit freier Oberfläche. Diese Klasse beinhaltet Probleme wie das Verhalten von Wellen an flachen Stränden oder die Bewegung einer Flutwelle in einem Fluss. Diese Beispiele zeigen deutlich die Notwendigkeit, den Einfluss von Topographie sowie die Behandlung von Nass/Trockenübergängen im Verfahren zu berücksichtigen. In der vorliegenden Dissertation wird ein, in Gebieten mit hinreichender Wasserhöhe, hochgenaues Finite-Volumen-Verfahren zur numerischen Bestimmung des zeitlichen Verlaufs der Lösung der zweidimensionalen Flachwassergleichung aus gegebenen Anfangs- und Randbedingungen auf einem unstrukturierten Gitter vorgestellt, welches in der Lage ist, den Einfluss topographischer Quellterme auf die Strömung zu berücksichtigen, sowie in sogenannten \glqq lake at rest\grqq-stationären Zuständen diesen Einfluss mit den numerischen Flüssen exakt auszubalancieren. Basis des Verfahrens ist ein Finite-Volumen-Ansatz erster Ordnung, welcher durch eine WENO Rekonstruktion unter Verwendung der Methode der kleinsten Quadrate und eine sogenannte Space Time Expansion erweitert wird mit dem Ziel, ein Verfahren beliebig hoher Ordnung zu erhalten. Die im Verfahren auftretenden Riemannprobleme werden mit dem Riemannlöser von Chinnayya, LeRoux und Seguin von 1999 gelöst, welcher die Einflüsse der Topographie auf den Strömungsverlauf mit berücksichtigt. Es wird in der Arbeit bewiesen, dass die Koeffizienten der durch das WENO-Verfahren berechneten Rekonstruktionspolynome die räumlichen Ableitungen der zu rekonstruierenden Funktion mit einem zur Verfahrensordnung passenden Genauigkeitsgrad approximieren. Ebenso wird bewiesen, dass die Koeffizienten des aus der Space Time Expansion resultierenden Polynoms die räumlichen und zeitlichen Ableitungen der Lösung des Anfangswertproblems approximieren. Darüber hinaus wird die wohlbalanciertheit des Verfahrens für beliebig hohe numerische Ordnung bewiesen. Für die Behandlung von Nass/Trockenübergangen wird eine Methode zur Ordnungsreduktion abhängig von Wasserhöhe und Zellgröße vorgeschlagen. Dies ist notwendig, um in der Rechnung negative Werte für die Wasserhöhe, welche als Folge von Oszillationen des Raum-Zeit-Polynoms auftreten können, zu vermeiden. Numerische Ergebnisse die die theoretische Verfahrensordnung bestätigen werden ebenso präsentiert wie Beispiele, welche die hervorragenden Eigenschaften des Gesamtverfahrens in der Berechnung herausfordernder Probleme demonstrieren.

A geostatistical analysis of soil, vegetation, and image data characterizing land surface variation

The elucidation of spatial variation in the landscape can indicate potential wildlife habitats or breeding sites for vectors, such as ticks or mosquitoes, which cause a range of diseases. Information from remotely sensed data could aid the delineation of vegetation distribution on the ground in areas where local knowledge is limited. The data from digital images are often difficult to interpret because of pixel-to-pixel variation, that is, noise, and complex variation at more than one spatial scale. Landsat Thematic Mapper Plus (ETM+) and Satellite Pour l'Observation de La Terre (SPOT) image data were analyzed for an area close to Douna in Mali, West Africa. The variograms of the normalized difference vegetation index (NDVI) from both types of image data were nested. The parameters of the nested variogram function from the Landsat ETM+ data were used to design the sampling for a ground survey of soil and vegetation data. Variograms of the soil and vegetation data showed that their variation was anisotropic and their scales of variation were similar to those of NDVI from the SPOT data. The short- and long-range components of variation in the SPOT data were filtered out separately by factorial kriging. The map of the short-range component appears to represent the patterns of vegetation and associated shallow slopes and drainage channels of the tiger bush system. The map of the long-range component also appeared to relate to broader patterns in the tiger bush and to gentle undulations in the topography. The results suggest that the types of image data analyzed in this study could be used to identify areas with more moisture in semiarid regions that could support wildlife and also be potential vector breeding sites.

Approximations to the scattering of water waves by steep topography

A new method is developed for approximating the scattering of linear surface gravity waves on water of varying quiescent depth in two dimensions. A conformal mapping of the fluid domain onto a uniform rectangular strip transforms steep and discontinuous bed profiles into relatively slowly varying, smooth functions in the transformed free-surface condition. By analogy with the mild-slope approach used extensively in unmapped domains, an approximate solution of the transformed problem is sought in the form of a modulated propagating wave which is determined by solving a second-order ordinary differential equation. This can be achieved numerically, but an analytic solution in the form of a rapidly convergent infinite series is also derived and provides simple explicit formulae for the scattered wave amplitudes. Small-amplitude and slow variations in the bedform that are excluded from the mapping procedure are incorporated in the approximation by a straightforward extension of the theory. The error incurred in using the method is established by means of a rigorous numerical investigation and it is found that remarkably accurate estimates of the scattered wave amplitudes are given for a wide range of bedforms and frequencies.

Flow-induced dynamic surface tension effects at nanoscale

The aim of this study is to investigate flow-induced dynamic surface tension effects, similar to the well-known Marangoni phenomena, but solely generated by the nanoscale topography of the substrates. The flow-induced surface tension effects are examined on the basis of a sharp interface theory. It is demonstrated how nanoscale objects placed at the boundary of the flow domain result in the generation of substantial surface forces acting on the bulk flow.

Hyperresolution global land surface modeling: meeting a grand challenge for monitoring Earth's terrestrial water

Monitoring Earth's terrestrial water conditions is critically important to many hydrological applications such as global food production; assessing water resources sustainability; and flood, drought, and climate change prediction. These needs have motivated the development of pilot monitoring and prediction systems for terrestrial hydrologic and vegetative states, but to date only at the rather coarse spatial resolutions (∼10–100 km) over continental to global domains. Adequately addressing critical water cycle science questions and applications requires systems that are implemented globally at much higher resolutions, on the order of 1 km, resolutions referred to as hyperresolution in the context of global land surface models. This opinion paper sets forth the needs and benefits for a system that would monitor and predict the Earth's terrestrial water, energy, and biogeochemical cycles. We discuss six major challenges in developing a system: improved representation of surface‐subsurface interactions due to fine‐scale topography and vegetation; improved representation of land‐atmospheric interactions and resulting spatial information on soil moisture and evapotranspiration; inclusion of water quality as part of the biogeochemical cycle; representation of human impacts from water management; utilizing massively parallel computer systems and recent computational advances in solving hyperresolution models that will have up to 109 unknowns; and developing the required in situ and remote sensing global data sets. We deem the development of a global hyperresolution model for monitoring the terrestrial water, energy, and biogeochemical cycles a “grand challenge” to the community, and we call upon the international hydrologic community and the hydrological science support infrastructure to endorse the effort.

On the variability of the surface environment response to synoptic forcing over complex terrain: a multivariate data analysis approach

Synoptic climatology relates the atmospheric circulation with the surface environment. The aim of this study is to examine the variability of the surface meteorological patterns, which are developing under different synoptic scale categories over a suburban area with complex topography. Multivariate Data Analysis techniques were performed to a data set with surface meteorological elements. Three principal components related to the thermodynamic status of the surface environment and the two components of the wind speed were found. The variability of the surface flows was related with atmospheric circulation categories by applying Correspondence Analysis. Similar surface thermodynamic fields develop under cyclonic categories, which are contrasted with the anti-cyclonic category. A strong, steady wind flow characterized by high shear values develops under the cyclonic Closed Low and the anticyclonic H–L categories, in contrast to the variable weak flow under the anticyclonic Open Anticyclone category.

Cooled infrared filters and dichroics for the sea and land surface temperature radiometer (SLSTR)

The Sea and Land Surface Temperature Radiometer (SLSTR) is a nine channel visible and infrared high precision radiometer designed to provide climate data of global sea and land surface temperatures. The SLSTR payload is destined to fly on the Ocean and Medium-Resolution Land Mission for the ESA/EU Global Monitoring for Environment and Security (GMES) Programme Sentinel-3 mission to measure the sea and land temperature and topography for near real-time environmental and atmospheric climate monitoring of the Earth. In this paper we describe the optical layout of infrared optics in the instrument, spectral thin-film multilayer design, and system channel throughput analysis for the combined interference filter and dichroic beamsplitter coatings to discriminate wavelengths at 3.74, 10.85 & 12.0 μm. The rationale for selection of thin-film materials, deposition technique, and environmental testing, inclusive of humidity, thermal cycling and ionizing radiation testing are also described.

A comparison of GOCE and drifter-based estimates of the North Atlantic steady-state surface circulation

Over the last decade, due to the Gravity Recovery And Climate Experiment (GRACE) mission and, more recently, the Gravity and steady state Ocean Circulation Explorer (GOCE) mission, our ability to measure the ocean’s mean dynamic topography (MDT) from space has improved dramatically. Here we use GOCE to measure surface current speeds in the North Atlantic and compare our results with a range of independent estimates that use drifter data to improve small scales. We find that, with filtering, GOCE can recover 70% of the Gulf Steam strength relative to the best drifter-based estimates. In the subpolar gyre the boundary currents obtained from GOCE are close to the drifter-based estimates. Crucial to this result is careful filtering which is required to remove small-scale errors, or noise, in the computed surface. We show that our heuristic noise metric, used to determine the degree of filtering, compares well with the quadratic sum of mean sea surface and formal geoid errors obtained from the error variance–covariance matrix associated with the GOCE gravity model. At a resolution of 100 km the North Atlantic mean GOCE MDT error before filtering is 5 cm with almost all of this coming from the GOCE gravity model.

How well can we measure the ocean’s mean dynamic topography from space?

Recent gravity missions have produced a dramatic improvement in our ability to measure the ocean’s mean dynamic topography (MDT) from space. To fully exploit this oceanic observation, however, we must quantify its error. To establish a baseline, we first assess the error budget for an MDT calculated using a 3rd generation GOCE geoid and the CLS01 mean sea surface (MSS). With these products, we can resolve MDT spatial scales down to 250 km with an accuracy of 1.7 cm, with the MSS and geoid making similar contributions to the total error. For spatial scales within the range 133–250 km the error is 3.0 cm, with the geoid making the greatest contribution. For the smallest resolvable spatial scales (80–133 km) the total error is 16.4 cm, with geoid error accounting for almost all of this. Relative to this baseline, the most recent versions of the geoid and MSS fields reduce the long and short-wavelength errors by 0.9 and 3.2 cm, respectively, but they have little impact in the medium-wavelength band. The newer MSS is responsible for most of the long-wavelength improvement, while for the short-wavelength component it is the geoid. We find that while the formal geoid errors have reasonable global mean values they fail capture the regional variations in error magnitude, which depend on the steepness of the sea floor topography.

Effect of uncertainty in surface mass balance--elevation feedback on projections of the future sea level contribution of the Greenland ice sheet

We apply a new parameterisation of the Greenland ice sheet (GrIS) feedback between surface mass balance (SMB: the sum of surface accumulation and surface ablation) and surface elevation in the MAR regional climate model (Edwards et al., 2014) to projections of future climate change using five ice sheet models (ISMs). The MAR (Modèle Atmosphérique Régional: Fettweis, 2007) climate projections are for 2000–2199, forced by the ECHAM5 and HadCM3 global climate models (GCMs) under the SRES A1B emissions scenario. The additional sea level contribution due to the SMB– elevation feedback averaged over five ISM projections for ECHAM5 and three for HadCM3 is 4.3% (best estimate; 95% credibility interval 1.8–6.9 %) at 2100, and 9.6% (best estimate; 95% credibility interval 3.6–16.0 %) at 2200. In all results the elevation feedback is significantly positive, amplifying the GrIS sea level contribution relative to the MAR projections in which the ice sheet topography is fixed: the lower bounds of our 95% credibility intervals (CIs) for sea level contributions are larger than the “no feedback” case for all ISMs and GCMs. Our method is novel in sea level projections because we propagate three types of modelling uncertainty – GCM and ISM structural uncertainties, and elevation feedback parameterisation uncertainty – along the causal chain, from SRES scenario to sea level, within a coherent experimental design and statistical framework. The relative contributions to uncertainty depend on the timescale of interest. At 2100, the GCM uncertainty is largest, but by 2200 both the ISM and parameterisation uncertainties are larger. We also perform a perturbed parameter ensemble with one ISM to estimate the shape of the projected sea level probability distribution; our results indicate that the probability density is slightly skewed towards higher sea level contributions.

Evidence of a topographic signal in surface soil moisture derived from ENVISAT ASAR wide swath data

The susceptibility of a catchment to flooding is affected by its soil moisture prior to an extreme rainfall event. While soil moisture is routinely observed by satellite instruments, results from previous work on the assimilation of remotely sensed soil moisture into hydrologic models have been mixed. This may have been due in part to the low spatial resolution of the observations used. In this study, the remote sensing aspects of a project attempting to improve flow predictions from a distributed hydrologic model by assimilating soil moisture measurements are described. Advanced Synthetic Aperture Radar (ASAR) Wide Swath data were used to measure soil moisture as, unlike low resolution microwave data, they have sufficient resolution to allow soil moisture variations due to local topography to be detected, which may help to take into account the spatial heterogeneity of hydrological processes. Surface soil moisture content (SSMC) was measured over the catchments of the Severn and Avon rivers in the South West UK. To reduce the influence of vegetation, measurements were made only over homogeneous pixels of improved grassland determined from a land cover map. Radar backscatter was corrected for terrain variations and normalized to a common incidence angle. SSMC was calculated using change detection. To search for evidence of a topographic signal, the mean SSMC from improved grassland pixels on low slopes near rivers was compared to that on higher slopes. When the mean SSMC on low slopes was 30–90%, the higher slopes were slightly drier than the low slopes. The effect was reversed for lower SSMC values. It was also more pronounced during a drying event. These findings contribute to the scant information in the literature on the use of high resolution SAR soil moisture measurement to improve hydrologic models.

SEM analysis of enamel surface treated by Er : YAG laser: Influence of irradiation distance

Background: Depending on the distance of laser tip to dental surface a specific morphological pattern should be expected. However, there have been limited reports that correlate the Er:YAG irradiation distance with dental morphology. Purpose: To assess the influence of Er:YAG laser irradiation distance on enamel morphology, by means of scanning electron microscopy (SEM). Methods: Sixty human third molars were employed to obtain discs (congruent to 1 mm thick) that were randomly assigned to six groups (n = 10). Five groups received Er:YAG laser irradiation (80 mJ/2 Hz) for 20 s, according to the irradiation distance: 11, 12, 14, 16, or 17 mm. and the control group was treated with 37% phosphoric acid for 15 s. The laser-irradiated discs were bisected. One hemi-disc was separated for superficial analysis without subsequent acid etching, and the other one, received the phosphoric acid for 15 s. Samples were prepared for SEM. Results: Laser irradiation at 11 and 12 min provided an evident ablation of enamel, with evident fissures and some fused areas. At 14, 16 and 17 mm the superficial topography was flatter than in the other distances. The subsequent acid etching on the lased-surface partially removed the disorganized tissue. Conclusions: Er:YAG laser in defocused mode promoted slight morphological alterations and seems more suitable for enamel conditioning than focused irradiation. The application of phosphoric acid on lased-enamel surface, regardless of the irradiation distance, decreased the superficial irregularities.

Multiscale Analysis of Topographic Surface Roughness in the Midland Valley, Scotland

Surface roughness is an important geomorphological variable which has been used in the Earth and planetary sciences to infer material properties, current/past processes, and the time elapsed since formation. No single definition exists; however, within the context of geomorphometry, we use surface roughness as an expression of the variability of a topographic surface at a given scale, where the scale of analysis is determined by the size of the landforms or geomorphic features of interest. Six techniques for the calculation of surface roughness were selected for an assessment of the parameter`s behavior at different spatial scales and data-set resolutions. Area ratio operated independently of scale, providing consistent results across spatial resolutions. Vector dispersion produced results with increasing roughness and homogenization of terrain at coarser resolutions and larger window sizes. Standard deviation of residual topography highlighted local features and did not detect regional relief. Standard deviation of elevation correctly identified breaks of slope and was good at detecting regional relief. Standard deviation of slope (SD(slope)) also correctly identified smooth sloping areas and breaks of slope, providing the best results for geomorphological analysis. Standard deviation of profile curvature identified the breaks of slope, although not as strongly as SD(slope), and it is sensitive to noise and spurious data. In general, SD(slope) offered good performance at a variety of scales, while the simplicity of calculation is perhaps its single greatest benefit.

Tide-topography interaction along the eastern Brazilian shelf

In the Tropics, continental shelves governed by western boundary currents are considered to be among the least productive ocean margins in the world, unless eddy-induced shelf-edge upwelling becomes significant. The eastern Brazilian shelf in the Southwest Atlantic is one of these, and since the slight nutrient input from continental sources is extremely oligotrophic. It is characterized by complex bathymetry with the presence of shallow banks and seamounts. In this work, a full three-dimensional nonlinear primitive equation ocean model is used to demonstrate that the interaction of tidal currents and the bottom topography of the east Brazil continental shelf is capable of producing local upwelling of South Atlantic Central Water, bringing nutrients up from deep waters to the surface layer. Such upper layer enrichment is found to be of significance in increasing local primary productivity. (c) 2005 Elsevier Ltd. All rights reserved.

Biological Performance of Chemical Hydroxyapatite Coating Associated With Implant Surface Modification by Laser Beam: Biomechanical Study in Rabbit Tibias

Purpose: Considering the potential of the association between laser ablation and smaller scale hydroxyapatite (HA) coatings to create a stable and bioactive surface on titanium dental implants, the aim of the present study was to determine, by the removal torque test, the effects of a surface treatment created by laser-ablation (Nd:YAG) and, later, thin deposition of HA particles by a chemical process, compared to implants with only laser-ablation and implants with machined surfaces.Materials and Methods: Forty-eight rabbits received I implant by tibia of the following surfaces: machined surface (MS), laser-modified surface (LMS), and biomimetic hydroxiapatite coated surface (HA). After 4, 8, and 12 weeks of healing, the removal torque was measured by a torque gauge. The surfaces studied were analyzed according to their topography, chemical composition, and roughness.Results: Average removal torque in each period was 23.28, 24.0, and 33.85 Ncm to MS, 33.0, 39.87, and 54.57 Ncm to LMS, and 55.42, 63.71 and 64.0 Ncm to HA. The difference was statistically significant (P < .05) between the LMS-MS and HA-MS surfaces in all periods of evaluation, and between LMS-HA to 4 and 8 weeks of healing. The surface characterization showed a deep, rough, and regular topography provided by the laser conditioning, that was followed by the HA coating.Conclusions: Based on these results, it was possible to conclude that the implants with laser surface modification associated with HA biomimetic coating can shorten the implant healing period by the increase of bone implant interaction during the first 2 months after implant placement. (C) 2009 American Association of Oral and Maxillofacial Surgeons J Oral Maxillofac Surg 67:1706-1715, 2009