Dynamical System Exploration of the Hurst Phenomenon in Simple Climate Models

Mesa, OJ; Gupta, VK; O'Connell, PE

doi:10.1029/2011GM001081

Dynamical System Exploration of the Hurst Phenomenon in Simple Climate Models

Lookup NU author(s): Professor Enda O'Connell

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Abstract

The Hurst phenomenon, which reflects long-term fluctuations in geophysical time series, has attracted the attention of the research community for nearly 60 years due to its practical and theoretical importance. Yet a geophysical understanding of the Hurst phenomenon has remained elusive despite mutually conflicting hypotheses of long-term memory and nonstationarity proposed in the hydrology literature. The hypothesis of long-term memory in the climate system has recently gathered support from climate scientists through the publication of spectra that are consistent with the Hurst phenomenon for decadal to centennial time scales. A possible geophysical basis for this statistical feature has been explored elsewhere using complex global climate models. Here we explore a complementary pathway by means of the dynamics of nonuniformly mixing systems. As these systems pass bifurcations, they can exhibit the characteristics of tipping points and critical transitions that are observed in many complex dynamical systems, ranging from ecosystems to financial markets and the climate. The specific case of a Hopf bifurcation, which marks the transition from a stable system to a cyclic system, is investigated using simple dynamical systems that have been used as climate models involving energy balance and negative feedback with and without the hydrological cycle. Analyses of the model simulations reveal complex nonstationary behavior that inhibits consistent interpretation of the Hurst exponent using three well-known estimation methods. Nonetheless, the results demonstrate that dynamical systems methods can play an important role in further work on understanding the links between climate dynamics, long-term memory, nonstationarity, and the Hurst phenomenon.