Proxy records from Greenland ice cores have been studied for several decades, yet many open questions remain regarding the climate variability encoded therein. Here, we use a Bayesian framework for inferring inverse, stochastic-dynamic models from δ 18 O and dust records of unprecedented, subdecadal temporal resolution. The records stem from the North Greenland Ice Core Project (NGRIP) and we focus on the time interval 59 ka-22 ka b2k. Our model reproduces the dynamical characteristics of both the δ 18 O and dust proxy records, including the millennial-scale Dansgaard-Oeschger variability, as well 5 as statistical properties such as probability density functions, waiting times and power spectra, with no need for any external forcing. The crucial ingredients for capturing these properties are (i) high-resolution training data; (ii) cubic drift terms; (iii) nonlinear coupling terms between the δ 18 O and dust time series; and (iv) non-Markovian contributions that represent shortterm memory effects.1 Introduction 10 Data-driven stochastic difference equation models have recently been successfully applied to a wide range of climatic phenomena (Kondrashov et al., , 2006Kravtsov et al., 2005Kravtsov et al., , 2009. The striking success of these authors' Empirical Model Reduction (EMR) approach in reproducing dynamical and statistical properties of the underlying dynamical systems has been explained by embedding EMR models in the larger class of multilayer stochastic models (MSMs); the latter models, in turn, were shown to be solidly grounded in the Mori-Zwanzig (MZ, (Zwanzig, 1964;Mori, 1965)) formalism of statistical physics 15 (Kondrashov et al., 2015). In addition to enhancing our understanding of the geophysical systems under consation, EMR-MSM models have also been shown to be well suited for predictive purposes; e.g., they have considerable skill in predicting 1 Earth Syst. Dynam. Discuss.,

Nonlinear time delay systems produce inherently delay-induced periodic oscillations, which are, however, too idealistic compared to observations. We exhibit a unified stochastic framework to systematically rectify such oscillations into oscillatory patterns with enriched temporal variabilities through generic, nonlinear responses to stochastic perturbations. Two paradigms of noise-driven chaos in high dimension are identified, fundamentally different from chaos triggered by parameter-space noise. Noteworthy is a low-dimensional stretch-and-fold mechanism, leading to stochastic strange attractors exhibiting horseshoe-like structures mirroring turbulent transport of passive tracers. The other is high-dimensional , with noise acting along the critical eigendirection and transmitted to “deeper” stable modes through nonlinearity, leading to stochastic attractors exhibiting swarm-like behaviors with power-law and scale break properties. The theory is applied to cloud delay models to parameterize missing physics such as intermittent rain and Lagrangian turbulent effects. The stochastically rectified model reproduces with fidelity complex temporal variabilities of open-cell oscillations exhibited by high-end cloud simulations.

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