150 research outputs found
Compressible viscoelastodynamics: the Longman (1963) paradox and the long period tangential flux
No full textThe compressible viscoelastodynamics and the fluid behaviour of the Earth occupy an important position in the study of glacial isostatic adjustments (GIA). There, our understanding of these issues is incomplete and we still have to solve the Longman (1963) paradox concerning compressible inviscid solids, in order to describe correctly viscoelastic solids at large time scales or the fluid outer core. For compositional stratifications (the density increase with depth deviates from what should be expected from self-compression) static perturbations cannot involve volume changes. Thus the incremental pressure vanishes and loads could not be sustained, at least from a mathematical point of view. This conclusion is not physically sound and, obviously, load are sustained isostatically. For compressional stratifications instead, incremental pressure is allowed. However the differential system describing conservation of momentum and self-gravitation is not well posed and thus it is not completely solved. Smylie {\amp} Manshina (1971) and Chinnery (1975) proposed a way to avoid the Longman (1963) paradox in order to define core-mantle boundary (CMB) conditions. For compressional stratifications, we set up the system of differential equations controlling the perturbations of the inviscid fluid and we propose a new way to derive the CMB conditions able to determine also spatial and gravitational perturbations. Furthermore, we derive a new analytical solution for compressible Maxwell Earth models characterized both by stable and unstable compositional stratifications, as well as by compressional stratifications. This allows us to discover a new class of relaxation modes, the compositional C-modes, of which the unstable Rayleigh-Taylor modes are a subclass. If the stratification is unstable these modes describe the well known gravitational overturning, while, for stable stratification, they describe a long period tangential flux, which diverges in the fluid limit. Our findings make a step ahead in the solution of the Longman (1963) paradox and shed new light on material compressibility and buoyancy forces
Compressible viscoelastodynamics of a spherical body at long timescales and its isostatic equilibrium
No full textThe problem of compressibility in modelling of viscoelastic deformations of planetary bodies is still a topic under discussion. Studies facing this topic discuss the error when considering a stratification of layers with constant material parameters. But homogeneous compressible layers imply that the initial state is not stable. So, any perturbationmethod applied to this type of state results in an ill-posed problem, evident in a denumerable infinite set of modes in the spectral representation of the solution. Based on the analytic solution of Cambiotti and Sabadini, we discuss any violation from the stable Adams-Williamson condition to result in unphysical behaviour where we concentrate here on the consequences for the horizontal displacement and deformation within the mantle due to surface loading. This focus motivates to revisit the Longman paradox, which discusses the boundary conditions for a compressible fluid core
Publication data for 'Willeit, M., Calov, R., Talento, S., Greve, R., Bernales, J., Klemann, V., Bagge, M., and Ganopolski, A.: Glacial inception through rapid ice area increase driven by albedo and vegetation feedbacks, EGUsphere [preprint], https://doi.org/10.5194/egusphere-2023-1462, 2023.'
No full text<p>Willeit, M., Calov, R., Talento, S., Greve, R., Bernales, J., Klemann, V., Bagge, M., and Ganopolski, A.: Glacial inception through rapid ice area increase driven by albedo and vegetation feedbacks, EGUsphere [preprint], https://doi.org/10.5194/egusphere-2023-1462, 2023. </p>
Applying local Green’s functions to study the influence of the crustal structure on hydrological loading displacements
No full textThe influence of the elastic Earth properties on seasonal or shorter periodic surface deformations due to atmospheric surface pressure and terrestrial water storage variations is usually modeled by applying a local half-space model or an one dimensional spherical Earth model like PREM from which a unique set of elastic load Love numbers, or alternatively, elastic Green's functions are derived. The first model is valid only if load and observer almost coincide, the second model considers only the response of an average Earth structure. However, for surface loads with horizontal scales less than 2500 km2, as for instance, for strong localized hydrological signals associated with heavy precipitation events and river floods, the Earth elastic response becomes very sensitive to inhomogeneities in the Earth crustal structure. We derive a set of local Green's functions defined globally on a 1° × 1° grid for the 3-layer crustal structure TEA12. Local Green's functions show standard deviations of ±12% in the vertical and ±21% in the horizontal directions for distances in the range from 0.1° to 0.5°. By means of Green's function scatter plots, we analyze the dependence of the load response to various crustal rocks and layer thicknesses. The application of local Green's functions instead of a mean global Green's function introduces a variability of 0.5–1.0 mm into the hydrological loading displacements, both in vertical and in horizontal directions. Maximum changes due to the local crustal structures are from −25% to +26% in the vertical and −91% to +55% in the horizontal displacements. In addition, the horizontal displacement can change its direction significantly. The lateral deviations in surface deformation due to local crustal elastic properties are found to be much larger than the differences between various commonly used one-dimensional Earth models
A benchmark study for glacial-isostatic adjustment codes
No full textThe study of Glacial Isostatic Adjustment (GIA) is gaining an increasingly im-portant role within the geophysical community. Understanding the response of the Earth to loading is crucial in various contexts, ranging from the the interpretation of modern satellite geodetic measurements (e. g. GRACE and GOCE) to the projections of future sea level trends in response to climate change. Modern modeling approaches to GIA are based on various techniques that range from purely analytical formulations to fully numerical methods. Despite various teams independently investigating GIA, we do not have a suitably large set of explicitly validated numerical results through which they may be validated; a community benchmark data set would clearly be valuable. Following the example of the mantle convection community, here we present, for the first time, the results of a benchmark study of codes designed to model GIA. The approaches benchmarked are based on significantly different codes and different techniques. This effort is performed within the Working Group 4 (WG4) of the ESF COST Action ES0701 “Improved constraints on models of Glacial Isostatic Adjustment”. Our aims are: i) testing the codes currently in use by the various teams, ii) establish a sufficiently large set of agreed results, iii) correct possible systematic errors embedded in the various physical formulations or computer implementations, and iv) facilitate the dissemination of numerical tools for surface loading studies to the community and to young scientists. The test computations are mainly based on models with spherical symmetry and Maxwell rheology and include inputs from various different methods and solution techniques: viscoelastic normal modes, spectral finite–elements and finite–elements. The tests involve the loading and tidal Love numbers and their relaxation spectra, the deformation and gravity variations driven by surface loads characterized by simple geometry and time–history, and the rotational fluctuations in response to glacial unloading. In spite of the significant differences in the numerical methods employed, the test computations show a satisfactory agreement between the results provided by the participants. Most of the existing misfits have been addressed during the preparation of the manuscript, some others are currently the subject of analysis within the WG4 community
Rijnstakingen - De oorzaken van de stakingen in de Rijnvaart tussen 1895 en 1935
No full textTussen 1895 en 1935 werd verschillende malen het werk onderbroken door werknemers en zelfstandige schippers in de Rijnscheepvaart. In dit onderzoek wordt onderzocht waarom deze Rijnstakingen plaatsvonden, door de verschillende factoren die daaraan ten grondslag lagen onder de loep te nemen. Deze factoren zijn onderverdeeld in economische, sociale en technologische factoren.
Met een Rijnstaking wordt een werkonderbrekingen van arbeiders en zelfstandige schippers die werkzaam waren in de Rijnvaart bedoeld. Zij legden het werk neer, namen geen vracht meer aan of maakten het anderen onmogelijk om hun werkzaamheden uit te voeren. Onder stakingen wordt nadrukkelijk ook het niet meer aannemen van vrachten door kleine Rijnschippers gerekend. De stakingen die in het onderzoek zijn meegenomen zijn onder andere stakingen in de havens aan de Rijn en stakingen onder het varend personeel op de Rijn, de bemanning van de schepen in het algemeen en bepaalde specialisaties daarbinnen in het bijzonder, zoals sleepbootpersoneel.
Tussen 1895 en 1935 varieerde de Rijnstakingen in aantal, intensiteit, omvang en de gevolgen. Tussen 1895 en 1912 hadden de stakingen meestal een plaatselijk karakter en ging het om zowel schippers als havenarbeiders. Tussen 1912 en 1918 werd nauwelijks gestaakt, waarna het aantal stakingen tussen 1918 en 1929 flink toenam. Vanaf 1929 tot 1935 was een afname zichtbaar, waarna na 1935 nauwelijks meer werd gestaakt.
De drie economische factoren die ten grondslag lagen aan de Rijnstakingen waren de daling van de prijs voor het vervoer over de Rijn, een hoge vraag naar transportruimte bij een laag aanbod en later een lage vraag naar transportruimte bij een hoog aanbod. Bij de laatste twee factoren was de onderhandelingspositie van de stakers essentieel.
De volgende vier sociale factoren droegen bij aan de stakingsbereidheid van de werknemers en zelfstandigen. Als eerste is gekeken naar solidariteit, wat is gemeten door te kijken naar het bestaan en functioneren van vak- en schippersbonden. Speciale aandacht gaat uit naar grensoverschrijdende solidariteit, omdat de Rijnvaart en de stakingen daarin zich niet tot landgrenzen beperkte. Hierna is gekeken naar onrust in de schippersbonden, naar de arbeidsomstandigheden en de invloed van Eerste Wereldoorlog op de stakingsbereidheid.
Als laatste is onderzocht in hoeverre technologische vernieuwingen hebben geleid tot stakingen. Zowel innovaties in de scheepsbouw als in de haven zijn onderzocht.
De uitkomst van het onderzoek is dat voornamelijk de economische en sociale ontwikkelingen aanleiding gaven om te staken. Technologische ontwikkelingen droegen in mindere mate bij, enkel de innovaties in de haven leidden tot stakingen. Daarnaast bleek dat de verschillende factoren dikwijls met elkaar interacteerde
Het jaar 1540: hitte en een keizerlijke eis
No full textOver het bezoek van Keizer Karel V in 1540 aan Haarle
Karel V liet steden zijn oorlogen betalen
No full textOver Haarlem en de staatsvorming door de Habsburger
Het jaar 1540: hitte en een keizerlijke eis
No full textOver het bezoek van Keizer Karel V in 1540 aan Haarle
A benchmark study of numerical implementations of the sea level equation in GIA modelling
No full textThe ocean load in glacial isostatic adjustment (GIA) modelling is represented by the so-called sea level equation (SLE). The SLE describes the mass redistribution of water between ice sheets and oceans on a deforming Earth. Despite various teams independently investigating GIA, there has been no systematic intercomparison among the numerical solvers of the SLE through which the methods may be validated. The goal of this paper is to present a series of synthetic examples designed for testing and comparing the numerical implementations of the SLE in GIA modelling. The 10 numerical codes tested combine various temporal and spatial parametrizations. The time-domain or Laplace-domain discretizations are used to solve the SLE through time, while spherical harmonics, finite differences or finite elements parametrize the GIA-related field variables spatially. The surface ice-water load and solid Earth’s topography are represented spatially either on an equiangular grid, a Gauss–Legendre or an equiarea grid with icosahedron-shaped spherical pixels. Comparisons are made in a series of five benchmark examples with an increasing degree of complexity. Due to the complexity of the SLE, there is no analytical solution to it. The accuracy of the numerical implementations is therefore assessed by the differences of the individual solutions with respect to a reference solution. While the benchmark study does not result in GIA predictions for a realistic loading scenario, we establish a set of agreed-upon results that can be extended in the future by including more complex case studies, such as solutions with realistic loading scenarios, the rotational feedback in the linear-momentum equation, and by considering a 3-D viscosity structure of the Earth’s mantle. The test computations performed so far show very good agreement between the individual results and their ability to capture the main features of sea-surface variation and the surface vertical displacement. The differences found can often be attributed to the different approximations inherent in the various algorithms. This shows the accuracy that can be expected from different implementations of the SLE, which helps to assess differences noted in the literature between predictions for realistic loading cases
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