Visual Analysis of Multiple Dynamic Sensitivities along Ascending Trajectories in the Atmosphere

Numerical weather prediction models rely on parameterizations for subgrid-scale processes, e.g., for cloud microphysics. These parameterizations are a well-known source of uncertainty in weather forecasts that can be quantified via algorithmic differentiation, which computes the sensitivities of prognostic variables to changes in model parameters. It is particularly interesting to use sensitivities to analyze the validity of physical assumptions on which microphysical parameterizations in the numerical model source code are based. In this article, we consider the use case of strongly ascending trajectories, so-called warm conveyor belt trajectories, known to have a significant impact on intense surface precipitation rates in extratropical cyclones. We present visual analytics solutions to analyze interactively the sensitivities of a selected prognostic variable, i.e. rain mass density, to multiple model parameters along such trajectories. We propose a visual interface that enables to a) compare the values of multiple sensitivities at a single time step on multiple trajectories, b) assess the spatio-temporal relationships between sensitivities and the shape and location of trajectories, and c) a comparative analysis of the temporal development of sensitivities along multiple trajectories. We demonstrate how our approach enables atmospheric scientists to interactively analyze the uncertainty in the microphysical parameterizations, and along the trajectories, with respect to a selected prognostic variable. We apply our approach to the analysis of convective trajectories within the extratropical cyclone "Vladiana", which occurred between 22-25 September 2016 over the North Atlantic

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quas ... pro consequendis in u.i. doctoralib. privilegiis & insignib. publice discutiendas proponit Hieronymus Christophorus Rheiner Ulm. Ad diem 7. Feb.Enthält 40 ThesenDiss. iur. Basel, 159

[Stammbuch Christoph Hieronymus Gugel <I.> (Fragment)]

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Bey dem 1734. Angetretenem Neuem Jahre, legte An Den Durchlauchtigsten Fürsten und Herrn, Herrn Ernst Augusten, Hertzogen zu Sachsen, Jülich, Cleve und Berg, ... Seinem gnädigsten regierenden Landes-Fürsten und Herrn, Aus aller unterthänigster Devotion Seinen Demüthigsten Glückwunsch ab in folgenden, Jhro Hoch-Fürstl. Durchl. unterthänigst-treu-gehorsamster Hieronym. Christoph. Meckbach, D.

Vorlageform des Erscheinungsvermerks: Jena, Gedruckt bey Johann Bernhard Heller

Mechanical energy balance and apparent fracture toughness for dykes in elastoplastic host rock with large-scale yielding

The dynamics of dyke emplacement are typically modelled by assuming an elastic rheology for the host rock. However, the resulting stress field predicts significant shear failure in the region surrounding the dyke tip. Here, we model the dyking process in an elastic-perfectly plastic host rock in order to simulate distributed shear fracturing and subsequent frictional slip on the fracture surfaces. The fluid mechanical aspects of the magma are neglected as we are interested only in the fracture mechanics of the process. Magma overpressure in dykes is typically of the same order of magnitude as the yield stress of the host rock in shear, especially when the pressure effect of volatiles exsolving from the magma is taken into account. Under these conditions, the plastic deformation zone has spatial dimensions that approach the length of the dyke itself, and concepts based on linear elastic fracture mechanics (LEFM) no longer apply. As incremental plasticity is path dependent, we describe two geologically meaningful endmember cases, namely dyke propagation at constant driving pressure, and gradual inflation of a pre-existing crack. For both models, we find that plastic deformation surrounding the fracture tip enhances dyke opening, and thus increases the energy input into the system due to pressure work integrated over the fracture wall. At the same time, energy is dissipated by plastic deformation. Dissipation in the propagation model is greater by about an order of magnitude than it is in the inflation model because the propagating dyke tip leaves behind it a broad halo of deformation due to plastic bending and unbending in the relict process zone. The net effect is that plastic deformation impedes dyke growth in the propagation model, while it enhances dyke growth in the inflation model. The results show that, when the plastic failure zone is large, a single parameter such as fracture toughness is unable to capture the physics that underpin the resistance of a fracture or dyke against propagation. In these cases, plastic failure has to be modelled explicitly for the given conditions. We provide analytical approximations for the propagation forces and the maximum dyke aperture for the two endmember cases, that is, the propagating dyke and the dyke formed by inflation of a crack. Furthermore, we show that the effect of plasticity on dyke energetics, together with an overestimate of magma pressure when interpreting dyke aspect ratios using elastic host rock models, offers a possible explanation for the long-standing paradox that laboratory measurements of fracture toughness of rocks consistently indicate values about two orders of magnitude lower than those derived from dyke observations.Title in thesis list of papers: Mechanical energy balance and fracture toughness for dykes in elastoplastic host rock</p

Effect of host-rock rheology on dyke shape, thickness and magma overpressure

The size and thickness of dykes is of fundamental importance for volcano dynamics because dykes are the primary path for magma transport, and because large numbers of dykes often comprise a major proportion of the volcanic edifice and of the underlying crust. Standard elastic models predict dyke geometry to be elliptic in cross-section for constant overpressure and uniform host-rock properties, whereas observations show that dyke thickness is typically more nearly constant with a sharp taper at the ends. Moreover, the predicted overpressures required to inflate dykes in a purely elastic medium are often significantly higher (&gt; 150 MPa and up to 2 GPa) than those estimated by other means (about 1-50 MPa). In this study, we use 2-D finite element models to test whether other host-rock rheologies lead to more realistic dyke shapes and overpressures. We examine three different rheologies, each of which is affected by the presence of the dyke itself: (1) elasticity with reduced moduli in regions of low pressure or tension; (2) elastoplasticity with plastic failure in the high-stress regions surrounding the dyke tips; (3) viscoelasticity with a viscosity decrease due to heating by the dyke. We use rheological parameters obtained from laboratory experiments whenever possible, and assume static conditions for the final dyke shape. We find that all three rheologies tend to make the dyke more rectangular relative to the elliptical dykes of the linearly elastic models. The change in shape is due to enhanced deformation in the high-stress zone surrounding the dyke tip. We also find that the overpressure required to inflate an initially thin dyke to a given thickness is reduced for all three rheologies. The greatest decrease in overpressure by a factor of about 0.1 is observed for the elastoplastic model, and for the viscoelastic model if the dyke intrudes into moderately pre-heated host-rock. We discuss our results with respect to dyke observations from Rum Island (Scotland) and use these as a guide to evaluate our models

De serierum reversione formulis analytico-combinatoriis exhibita specimen : quod amplissimi philosophorum ordinis auctoritate ... ad disceptandum proponit

Hieronymus Christophorus Vilelmus Eschenbach ... respondente Ioanne Michael Pflu