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Aus dem Inhalt: Einleitung Kapitel 1. Starke Gesetze der Grossen Zahlen 1. SGGZ unter Wachstumsbedingungen an die p-ten Momente 2. SGGZ für identisch verteilte Zufallsvariablen 3. SGGZ für Prozesse mit *-mixing-Eigenschaft Kapitel 2. Einführung zu diskreten (Sub-,Super-)Martingalen 1. Vorhersagbarkeit 2. gestoppte (Sub-,Super-)Martingale 3. Upcrossings 4. Konvergenzsätze 5. Doob-Zerlegung 6. Eine äquivalente Definition eines (Sub-)Martingals Kapitel 3. Martingale und gleichgradige Integrierbarkeit 1. Gleichmäßige(-f¨ormige,-gradige) Integrierbarkeit 2. gleichgradig integrierbare Martingale Kapitel 4. Martingale und das SGGZ Kapitel 5.”reversed“ (Sub-,Super-)Martingale 1. Konvergenzsätze Kapitel 6. (Sub-,Super-)Martingale mit gerichteter Indexmenge 1. Äquivalente Formulierung eines (Sub-)Martingals 2. Konvergenzsätze Kapitel 7. Quasimartingale,Amarts und Semiamarts 1. Konvergenzsätze 2. Riesz-Zerlegung 3. Doob-Zerlegung Kapitel 8. Amarts und das SGGZ Kapitel 9.”reversed“ Amarts und Semiamarts 1. Konvergenzsätze 2.”Aufwärts“- gegen ”Abwärts“-Adaptiertheit 3. Riesz-Zerlegung 4. Stabilitätsanalyse Kapitel 10. Amarts mit gerichteter Indexmenge 1. Konvergenzsätze 2. Riesz-Zerlegung Anhang A. zur Existenz einer Folge unabhängiger Zufallsvariablen B. Konvergenz
Ten ice-sheet models are used to study sensitivity of the Greenland and Antarctic ice sheets to prescribed changes of surface mass balance, sub-ice-shelf melting and basal sliding. Results exhibit a large range in projected contributions to sea-level change. In most cases, the ice volume above flotation lost is linearly dependent on the strength of the forcing. Combinations of forcings can be closely approximated by linearly summing the contributions from single forcing experiments, suggesting that nonlinear feedbacks are modest. Our models indicate that Greenland is more sensitive than Antarctica to likely atmospheric changes in temperature and precipitation, while Antarctica is more sensitive to increased ice-shelf basal melting. An experiment approximating the Intergovernmental Panel on Climate Change's RCP8.5 scenario produces additional first-century contributions to sea level of 22.3 and 8.1 cm from Greenland and Antarctica, respectively, with a range among models of 62 and 14 cm, respectively. By 200 years, projections increase to 53.2 and 26.7 cm, respectively, with ranges of 79 and 43 cm. Linear interpolation of the sensitivity results closely approximates these projections, revealing the relative contributions of the individual forcings on the combined volume change and suggesting that total ice-sheet response to complicated forcings over 200 years can be linearized.
The Sea-level Response to Ice Sheet Evolution (SeaRISE) effort explores the sensitivity of the current generation of ice sheet models to external forcing to gain insight into the potential future contribution to sea level from the Greenland and Antarctic ice sheets. All participating models simulated the ice sheet response to three types of external forcings: a change in oceanic condition, a warmer atmospheric environment, and enhanced basal lubrication. Here an analysis of the spatial response of the Greenland ice sheet is presented, and the impact of model physics and spin-up on the projections is explored. Although the modeled responses are not always homogeneous, consistent spatial trends emerge from the ensemble analysis, indicating distinct vulnerabilities of the Greenland ice sheet. There are clear response patterns associated with each forcing, and a similar mass loss at the full ice sheet scale will result in different mass losses at the regional scale, as well as distinct thickness changes over the ice sheet. All forcings lead to an increased mass loss for the coming centuries, with increased basal lubrication and warmer ocean conditions affecting mainly outlet glaciers, while the impacts of atmospheric forcings affect the whole ice sheet.
Homotherium was a genus of large-bodied scimitar-toothed cats, morphologically distinct from any extant felid species, that went extinct at the end of the Pleistocene [1-4]. They possessed large, saber-form serrated canine teeth, powerful forelimbs, a sloping back, and an enlarged optic bulb, all of which were key characteristics for predation on Pleistocene megafauna [5]. Previous mitochondrial DNA phylogenies suggested that it was a highly divergent sister lineage to all extant cat species [6-8]. However, mitochondrial phylogenies can be misled by hybridization [9], incomplete lineage sorting (ILS), or sex-biased dispersal patterns [10], which might be especially relevant for Homotherium since widespread mito-nuclear discrepancies have been uncovered in modern cats [10]. To examine the evolutionary history of Homotherium, we generated a -7x nuclear genome and a similar to 38x exome from H. latidens using shotgun and target-capture sequencing approaches. Phylogenetic analyses reveal Homotherium as highly divergent (similar to 22.5 Ma) from living cat species, with no detectable signs of gene flow. Comparative genomic analyses found signatures of positive selection in several genes, including those involved in vision, cognitive function, and energy consumption, putatively consistent with diurnal activity, well-developed social behavior, and cursorial hunting [5]. Finally, we uncover relatively high levels of genetic diversity, suggesting that Homotherium may have been more abundant than the limited fossil record suggests [3, 4, 11-14]. Our findings complement and extend previous inferences from both the fossil record and initial molecular studies, enhancing our understanding of the evolution and ecology of this remarkable lineage.
Anthropogenic climate change is likely to cause continuing global sea level rise(1), but some processes within the Earth system may mitigate the magnitude of the projected effect. Regional and global climate models simulate enhanced snowfall over Antarctica, which would provide a direct offset of the future contribution to global sea level rise from cryospheric mass loss(2,3) and ocean expansion(4). Uncertainties exist in modelled snowfall(5), but even larger uncertainties exist in the potential changes of dynamic ice discharge from Antarctica(1,6) and thus in the ultimate fate of the precipitation-deposited ice mass. Here we show that snowfall and discharge are not independent, but that future ice discharge will increase by up to three times as a result of additional snowfall under global warming. Our results, based on an ice-sheet model(7) forced by climate simulations through to the end of 2500 (ref. 8), show that the enhanced discharge effect exceeds the effect of surface warming as well as that of basal ice-shelf melting, and is due to the difference in surface elevation change caused by snowfall on grounded versus floating ice. Although different underlying forcings drive ice loss from basal melting versus increased snowfall, similar ice dynamical processes are nonetheless at work in both; therefore results are relatively independent of the specific representation of the transition zone. In an ensemble of simulations designed to capture ice-physics uncertainty, the additional dynamic ice loss along the coastline compensates between 30 and 65 per cent of the ice gain due to enhanced snowfall over the entire continent. This results in a dynamic ice loss of up to 1.25 metres in the year 2500 for the strongest warming scenario. The reported effect thus strongly counters a potential negative contribution to global sea level by the Antarctic Ice Sheet.
Recently observed large-scale disintegration of Antarctic ice shelves has moved their fronts closer towards grounded ice. In response, ice-sheet discharge into the ocean has accelerated, contributing to global sea-level rise and emphasizing the importance of calving-front dynamics. The position of the ice front strongly influences the stress field within the entire sheet-shelf-system and thereby the mass flow across the grounding line. While theories for an advance of the ice-front are readily available, no general rule exists for its retreat, making it difficult to incorporate the retreat in predictive models. Here we extract the first-order large-scale kinematic contribution to calving which is consistent with large-scale observation. We emphasize that the proposed equation does not constitute a comprehensive calving law but represents the first-order kinematic contribution which can and should be complemented by higher order contributions as well as the influence of potentially heterogeneous material properties of the ice. When applied as a calving law, the equation naturally incorporates the stabilizing effect of pinning points and inhibits ice shelf growth outside of embayments. It depends only on local ice properties which are, however, determined by the full topography of the ice shelf. In numerical simulations the parameterization reproduces multiple stable fronts as observed for the Larsen A and B Ice Shelves including abrupt transitions between them which may be caused by localized ice weaknesses. We also find multiple stable states of the Ross Ice Shelf at the gateway of the West Antarctic Ice Sheet with back stresses onto the sheet reduced by up to 90 % compared to the present state.
Insight into how environmental change determines the production and distribution of cyanobacterial toxins is necessary for risk assessment. Management guidelines currently focus on hepatotoxins (microcystins). Increasing attention is given to other classes, such as neurotoxins (e.g., anatoxin-a) and cytotoxins (e.g., cylindrospermopsin) due to their potency. Most studies examine the relationship between individual toxin variants and environmental factors, such as nutrients, temperature and light. In summer 2015, we collected samples across Europe to investigate the effect of nutrient and temperature gradients on the variability of toxin production at a continental scale. Direct and indirect effects of temperature were the main drivers of the spatial distribution in the toxins produced by the cyanobacterial community, the toxin concentrations and toxin quota. Generalized linear models showed that a Toxin Diversity Index (TDI) increased with latitude, while it decreased with water stability. Increases in TDI were explained through a significant increase in toxin variants such as MC-YR, anatoxin and cylindrospermopsin, accompanied by a decreasing presence of MC-LR. While global warming continues, the direct and indirect effects of increased lake temperatures will drive changes in the distribution of cyanobacterial toxins in Europe, potentially promoting selection of a few highly toxic species or strains.
The largest uncertainty in projections of future sea-level change results from the potentially changing dynamical ice discharge from Antarctica. Basal ice-shelf melting induced by a warming ocean has been identified as a major cause for additional ice flow across the grounding line. Here we attempt to estimate the uncertainty range of future ice discharge from Antarctica by combining uncertainty in the climatic forcing, the oceanic response and the ice-sheet model response. The uncertainty in the global mean temperature increase is obtained from historically constrained emulations with the MAGICC-6.0 (Model for the Assessment of Greenhouse gas Induced Climate Change) model. The oceanic forcing is derived from scaling of the subsurface with the atmospheric warming from 19 comprehensive climate models of the Coupled Model Intercomparison Project (CMIP-5) and two ocean models from the EU-project Ice2Sea. The dynamic ice-sheet response is derived from linear response functions for basal ice-shelf melting for four different Antarctic drainage regions using experiments from the Sea-level Response to Ice Sheet Evolution (SeaRISE) intercomparison project with five different Antarctic ice-sheet models. The resulting uncertainty range for the historic Antarctic contribution to global sea-level rise from 1992 to 2011 agrees with the observed contribution for this period if we use the three ice-sheet models with an explicit representation of ice-shelf dynamics and account for the time-delayed warming of the oceanic subsurface compared to the surface air temperature. The median of the additional ice loss for the 21st century is computed to 0.07 m (66% range: 0.02-0.14 m; 90% range: 0.0-0.23 m) of global sea-level equivalent for the low-emission RCP-2.6 (Representative Concentration Pathway) scenario and 0.09 m (66% range: 0.04-0.21 m; 90% range: 0.01-0.37 m) for the strongest RCP-8.5. Assuming no time delay between the atmospheric warming and the oceanic subsurface, these values increase to 0.09 m (66% range: 0.04-0.17 m; 90% range: 0.02-0.25 m) for RCP-2.6 and 0.15 m (66% range: 0.07-0.28 m; 90% range: 0.04-0.43 m) for RCP-8.5. All probability distributions are highly skewed towards high values. The applied ice-sheet models are coarse resolution with limitations in the representation of grounding-line motion. Within the constraints of the applied methods, the uncertainty induced from different ice-sheet models is smaller than that induced by the external forcing to the ice sheets.
We present the Potsdam Parallel Ice Sheet Model (PISM-PIK), developed at the Potsdam Institute for Climate Impact Research to be used for simulations of large-scale ice sheet-shelf systems. It is derived from the Parallel Ice Sheet Model (Bueler and Brown, 2009). Velocities are calculated by superposition of two shallow stress balance approximations within the entire ice covered region: the shallow ice approximation (SIA) is dominant in grounded regions and accounts for shear deformation parallel to the geoid. The plug-flow type shallow shelf approximation (SSA) dominates the velocity field in ice shelf regions and serves as a basal sliding velocity in grounded regions. Ice streams can be identified diagnostically as regions with a significant contribution of membrane stresses to the local momentum balance. All lateral boundaries in PISM-PIK are free to evolve, including the grounding line and ice fronts. Ice shelf margins in particular are modeled using Neumann boundary conditions for the SSA equations, reflecting a hydrostatic stress imbalance along the vertical calving face. The ice front position is modeled using a subgrid-scale representation of calving front motion (Albrecht et al., 2011) and a physically-motivated calving law based on horizontal spreading rates. The model is tested in experiments from the Marine Ice Sheet Model Intercomparison Project (MISMIP). A dynamic equilibrium simulation of Antarctica under present-day conditions is presented in Martin et al. (2011).
We present a dynamic equilibrium simulation of the ice sheet-shelf system on Antarctica with the Potsdam Parallel Ice Sheet Model (PISM-PIK). The simulation is initialized with present-day conditions for bed topography and ice thickness and then run to steady state with constant present-day surface mass balance. Surface temperature and sub-shelf basal melt distribution are parameterized. Grounding lines and calving fronts are free to evolve, and their modeled equilibrium state is compared to observational data. A physically-motivated calving law based on horizontal spreading rates allows for realistic calving fronts for various types of shelves. Steady-state dynamics including surface velocity and ice flux are analyzed for whole Antarctica and the Ronne-Filchner and Ross ice shelf areas in particular. The results show that the different flow regimes in sheet and shelves, and the transition zone between them, are captured reasonably well, supporting the approach of superposition of SIA and SSA for the representation of fast motion of grounded ice. This approach also leads to a natural emergence of sliding-dominated flow in stream-like features in this new 3-D marine ice sheet model.