Simple stochastic models for glacial dynamics

Abstract

[1] Glacial-interglacial events have several nonlinear and stochastic characteristics. Recent studies suggested additional stochastic nonlinear features (not necessarily related to the large-scale dynamics of the glacial cycle) in the timescale of 1-100 kyr including (1) strong long-range correlations in the magnitude of climate variable increments as well as (2) a wide multifractal spectrum. Realistic climate models should reproduce these properties of the natural system. We first study several previously proposed stochastic models for glacial-interglacial dynamics and demonstrate that they do not reproduce some of the nonlinear properties of the paleoclimate proxy data. We then suggest two nonlinear stochastic models for glacial-interglacial dynamics that exhibit similar stochastic nonlinear properties to those seen in the natural data. We conjecture that interaction between fast random fluctuations (representing atmospheric variability) and slowly varying fluctuations (representing oceanic variability) may underlie the observed stochastic nonlinearity of time series for glacial-interglacial oscillations.

Long‐term memory in 1000‐year simulated temperature records

“…Huybers and Curry [2006] [39] Finally, in this paper, we only studied temperature records and focused exclusively on the linear correlation properties. It is an interesting question how far the global climate models are able to reproduce also the nonlinear ''multifractal'' features of the climate system [see KoscielnyBunde et al, 1998;Weber and Talkner, 2001;Govindan et al, 2003;Ashkenazy et al, 2005;Bartos and Jánosi, 2006;Livina et al, 2007]. It is known that in particular rainfall is significantly multifractal [see, e.g., Tessier et al, 1996;Kantelhardt et al, 2006], and it will be interesting to see if this feature is also reflected in model rain fall data.…”

Appropriateness of correlated first-order auto-regressive processes for modeling daily temperature records

“…However, this does not necessarily imply NLCAR(1) and CAR(1) have similar volatile correlations. Recent studies [15] have used nonlinear stochastic models successfully to model glacial dynamics also reflected in long-range volatile correlations. Encouraged by previous findings [4,7,15] and results presented in [1], we believe that NLCAR(1) may be a more appropriate model to capture dynamics of daily temperature records.…”

Bifurcation structure and noise‐assisted transitions in the Pleistocene glacial cycles

“…These range from self‐sustained nonlinear oscillators [ Källen et al , 1979; Saltzman and Sutera , 1987; Gildor and Tziperman , 2000], forced nonlinear oscillators [ LeTreut and Ghil , 1983] to stochastic or coherence resonance [ Benzi et al , 1982; Pelletier , 2003]. Others emphasize, on the basis of spectral analysis, the nonlinear nature [ Rial , 1999] and the stochastic nature of the climate signal [ Kominz and Pisias , 1979; Ashkenazy et al , 2005].…”