Many palaeoclimate records from the North Atlantic region show a pattern of rapid climate oscillations, the so-called DansgaardOeschger events, with a quasi-periodicity of ,1,470 years for the late glacial period [1][2][3][4][5][6] . Various hypotheses have been suggested to explain these rapid temperature shifts, including internal oscillations in the climate system and external forcing, possibly from the Sun 7 . But whereas pronounced solar cycles of ,87 and ,210 years are well known [8][9][10][11][12] , a ,1,470-year solar cycle has not been detected 8 . Here we show that an intermediate-complexity climate model with glacial climate conditions simulates rapid climate shifts similar to the Dansgaard-Oeschger events with a spacing of 1,470 years when forced by periodic freshwater input into the North Atlantic Ocean in cycles of ,87 and ,210 years. We attribute the robust 1,470-year response time to the superposition of the two shorter cycles, together with strongly nonlinear dynamics and the long characteristic timescale of the thermohaline circulation. For Holocene conditions, similar events do not occur. We conclude that the glacial 1,470-year climate cycles could have been triggered by solar forcing despite the absence of a 1,470-year solar cycle.The onset of successive Dansgaard-Oeschger (DO) events, as documented in Greenland ice-cores 1,2 for example, is typically spaced by ,1,470 years or integer multiples thereof 13,14 . Because deviations from this cyclicity are small, often less than 100-200 years 15 , external forcing (solar or orbital) was suggested to trigger DO events 6,15,16 . However, neither orbital nor solar forcing shows a 1,470-year frequency. Spectral analysis performed on records of cosmogenic nuclides [8][9][10][11] , which are commonly used as proxies for solar variability 12 , indicates the possible existence of pronounced and stable 10,11 centennial-scale solar cycles (the DeVries-Suess and Gleissberg cycles with periods near 210 and 87 years 10,11 ) but does not reveal a 1,470-year cycle 8 . However, the DeVries and Gleissberg cycles are close to prime factors of 1,470 years (1,470/7 ¼ 210; 1,470/17 < 86.5). The superposition of two such frequencies could result in variability that repeats with a 1,470-year period.Here we propose that these two solar frequencies could have synchronized the glacial 1,470-year climate cycle. Support for the idea that a multi-century climate cycle might be linked with centuryscale solar variability comes from Holocene data: a multi-centennial drift-ice cycle in the North Atlantic was reported 17 to coincide with "rapid (100-to 200-year), conspicuously large-amplitude variations" in the production rates of the cosmogenic isotopes 14 C and 10 Be. To test our hypothesis, we force the coupled climate system model CLIMBER-2 (version 3) with the two solar frequencies. Earlier simulations with this model showed that, when forced by periodic and/or stochastic variations in the freshwater flux into the northern Atlantic, abrupt glacial warming events are triggere...

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 5 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 as-10 pects 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 15 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 20 advance in order to develop more adequate methods to test the statistical significance and the origin of the proposed glacial 1470-year climate cycle.Correspondence to: H. Braun (Holger.Braun@iup.uni-heidelberg.de) 45 acteristic timing of DO events, including coherence resonance (Ganopolski and Rahmstorf, 2002;Timmermann et al., 2003;Ditlevsen et al., 2005) and stochastic resonance (Alley et al., 2001a,b;Ganopolski and Rahmstorf, 2002;Rahmstorf and Alley, 2002).2 Spectrum of models DO events have already been simulated by a variety of models, ranging from simple conceptual ones 50 to Earth system models of intermediate complexity (EMICs). Conceptual models are most suitable to perform large numbers of long-term investigations because they require very little computational cost. However, they are often based on ad-hoc assumptions and only consider processes in a highly simplified way. In addition to that, the number of adjustable parameters is typically large compared to the degrees of freedom in those models. This implies that seemingly good results can often be 55 obtained merely by excessive tuning. Nevertheless, conceptual models can provide important help for the interpretation of complex climatic processes. 2The gap between conceptual models and the most comprehensive general circulation models (GCMs), which are not yet applicable for millennial-scale simulations because of their large co...

[1] North Atlantic climate during glacial times was characterized by large-amplitude switchings, the DansgaardOeschger (DO) events, with an apparent tendency to recur preferably in multiples of about 1470 years. Recent work interpreted these intervals as resulting from a subharmonic response of a highly nonlinear system to quasi-periodic solar forcing plus noise. This hypothesis was challenged as inconsistent with the observed variability in the phase relation between proxies of solar activity and Greenland climate. Here we reject the claim of inconsistency by showing that this phase variability is a robust, generic feature of the nonlinear dynamics of DO events, as described by a model. This variability is expected from the fact that the events are threshold crossing events, resulting from a cooperative process between the periodic forcing and the noise. This process produces a fluctuating phase relation with the periodic forcing, consistent with proxies of solar activity and Greenland climate.