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    A simple conceptual model of abrupt glacial climate events
    (Göttingen : Copernicus GmbH, 2007) Braun, H.; Ganopolski, A.; Christl, M.; Chialvo, D.R.
    Here we use a very simple conceptual model in an attempt to reduce essential parts of the complex nonlinearity of abrupt glacial climate changes (the so-called Dansgaard-Oeschger events) to a few simple principles, namely (i) the existence of two different climate states, (ii) a threshold process and (iii) an overshooting in the stability of the system at the start and the end of the events, which is followed by a millennial-scale relaxation. By comparison with a so-called Earth system model of intermediate complexity (CLIMBER-2), in which the events represent oscillations between two climate states corresponding to two fundamentally different modes of deep-water formation in the North Atlantic, we demonstrate that the conceptual model captures fundamental aspects of the nonlinearity of the events in that model. We use the conceptual model in order to reproduce and reanalyse nonlinear resonance mechanisms that were already suggested in order to explain the characteristic time scale of Dansgaard-Oeschger events. In doing so we identify a new form of stochastic resonance (i.e. an overshooting stochastic resonance) and provide the first explicitly reported manifestation of ghost resonance in a geosystem, i.e. of a mechanism which could be relevant for other systems with thresholds and with multiple states of operation. Our work enables us to explicitly simulate realistic probability measures of Dansgaard-Oeschger events (e.g. waiting time distributions, which are a prerequisite for statistical analyses on the regularity of the events by means of Monte-Carlo simulations). We thus think that our study is an important advance in order to develop more adequate methods to test the statistical significance and the origin of the proposed glacial 1470-year climate cycle.
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    Forced versus coupled dynamics in Earth system modelling and prediction
    (Göttingen : Copernicus GmbH, 2005) Knopf, B.; Held, H.; Schellnhuber, H.J.
    We compare coupled nonlinear climate models and their simplified forced counterparts with respect to predictability and phase space topology. Various types of uncertainty plague climate change simulation, which is, in turn, a crucial element of Earth System modelling. Since the currently preferred strategy for simulating the climate system, or the Earth System at large, is the coupling of sub-system modules (representing, e.g. atmosphere, oceans, global vegetation), this paper explicitly addresses the errors and indeterminacies generated by the coupling procedure. The focus is on a comparison of forced dynamics as opposed to fully, i.e. intrinsically, coupled dynamics. The former represents a particular type of simulation, where the time behaviour of one complex systems component is prescribed by data or some other external information source. Such a simplifying technique is often employed in Earth System models in order to save computing resources, in particular when massive model inter-comparisons need to be carried out. Our contribution to the debate is based on the investigation of two representative model examples, namely (i) a low-dimensional coupled atmosphere-ocean simulator, and (ii) a replica-like simulator embracing corresponding components. Whereas in general the forced version (ii) is able to mimic its fully coupled counterpart (i), we show in this paper that for a considerable fraction of parameter- and state-space, the two approaches qualitatively differ. Here we take up a phenomenon concerning the predictability of coupled versus forced models that was reported earlier in this journal: the observation that the time series of the forced version display artificial predictive skill. We present an explanation in terms of nonlinear dynamical theory. In particular we observe an intermittent version of artificial predictive skill, which we call on-off synchronization, and trace it back to the appearance of unstable periodic orbits. We also find it to be governed by a scaling law that allows us to estimate the probability of artificial predictive skill. In addition to artificial predictability we observe artificial bistability for the forced version, which has not been reported so far. The results suggest that bistability and intermittent predictability, when found in a forced model set-up, should always be cross-validated with alternative coupling designs before being taken for granted.