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- ItemTracing the Snowball bifurcation of aquaplanets through time reveals a fundamental shift in critical-state dynamics(Göttingen : Copernicus, 2023) Feulner, Georg; Bukenberger, Mona; Petri, StefanThe instability with respect to global glaciation is a fundamental property of the climate system caused by the positive ice-albedo feedback. The atmospheric concentration of carbon dioxide (CO2) at which this Snowball bifurcation occurs changes through Earth's history, most notably because of the slowly increasing solar luminosity. Quantifying this critical CO2 concentration is not only interesting from a climate dynamics perspective but also constitutes an important prerequisite for understanding past Snowball Earth episodes, as well as the conditions for habitability on Earth and other planets. Earlier studies are limited to investigations with very simple climate models for Earth's entire history or studies of individual time slices carried out with a variety of more complex models and for different boundary conditions, making comparisons and the identification of secular changes difficult. Here, we use a coupled climate model of intermediate complexity to trace the Snowball bifurcation of an aquaplanet through Earth's history in one consistent model framework. We find that the critical CO2 concentration decreased more or less logarithmically with increasing solar luminosity until about 1 billion years ago but dropped faster in more recent times. Furthermore, there was a fundamental shift in the dynamics of the critical state about 1.2 billion years ago (unrelated to the downturn in critical CO2 values), driven by the interplay of wind-driven sea-ice dynamics and the surface energy balance: for critical states at low solar luminosities, the ice line lies in the Ferrel cell, stabilised by the poleward winds despite moderate meridional temperature gradients under strong greenhouse warming. For critical states at high solar luminosities, on the other hand, the ice line rests at the Hadley cell boundary, stabilised against the equatorward winds by steep meridional temperature gradients resulting from the increased solar energy input at lower latitudes and stronger Ekman transport in the ocean.
- ItemMulti-parameter uncertainty analysis of a bifurcation point(Göttingen : Copernicus GmbH, 2006) Knopf, B.; Flechsig, M.; Zickfeld, K.Parameter uncertainty analysis of climate models has become a standard approach for model validation and testing their sensitivity. Here we present a novel approach that allows one to estimate the robustness of a bifurcation point in a multi-parameter space. In this study we investigate a box model of the Indian summer monsoon that exhibits a saddle-node bifurcation against those parameters that govern the heat balance of the system. The bifurcation brings about a change from a wet summer monsoon regime to a regime that is characterised by low precipitation. To analyse the robustness of the bifurcation point itself and its location in parameter space, we perform a multi-parameter uncertainty analysis by applying qualitative, Monte Carlo and deterministic methods that are provided by a multi-run simulation environment. Our results show that the occurrence of the bifurcation point is robust over a wide range of parameter values. The position of the bifurcation, however, is found to be sensitive on these specific parameter choices.
- ItemOn freshwater-dependent bifurcations in box models of the interhemispheric thermohaline circulation(Abingdon : Taylor and Francis Ltd., 2002) Titz, S.; Kuhlbrodt, T.; Rahmstorf, S.; Feudel, U.Conceptual box models of the interhemispheric thermohaline circulation are studied with respect to bifurcations. Freshwater fluxes are the main control parameters of the system: they determine the stable states and transitions between stable states of the large-scale thermohaline circulation. In this study of interhemispheric box models both numerical and analytical methods are used to investigate transition mechanisms of the thermohaline circulation. The box model examined first is an interhemispheric four-box model. It is shown that the two bifurcations where the present THC can become unstable, the saddle-node and the Hopf bifurcation, depend in a different way on hemispheric freshwater fluxes. A reduction of the model variables leads to the conclusion that two fixed freshwater fluxes between three surface boxes are the model feature responsible for the bifurcation behavior found. The significance of the Hopf bifurcation for the stability of the thermohaline circulation is discussed.
- ItemPolarization properties in the transition from below to above lasing threshold in broad-area vertical-cavity surface-emitting lasers(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Schulz-Ruhtenberg, Malte; Babushkin, Ihar; Loiko, Natalia Aleksandrovna; Huang, K.F.; Ackemann, T.For highly divergent emission of broad-area vertical-cavity surface-emitting lasers (VCSELs) a rotation of the polarization direction by up to 90 degrees occurs when the pump rate approaches the lasing threshold. Well below threshold the polarization is parallel to the direction of the transverse wave vector and is determined by the transmissive properties of the Bragg reflectors that form the cavity mirrors. In contrast, near-threshold and above-threshold emission is more affected by the reflective properties of the reflectors and is predominantly perpendicular to the direction of transverse wave vectors. Two qualitatively different types of polarization transition are demonstrated: an abrupt transition, where the light polarization vanishes at the point of the transition, and a smooth one, where it is significantly nonzero during the transition.