Long-range memory in internal and forced dynamics of millennium-long climate model simulations

L Østvand,T Nilsen,K Rypdal,D Divine,M Rypdal

doi:10.5194/esd-5-295-2014

Abstract

Abstract. Northern Hemisphere (NH) temperature records from a palaeoclimate reconstruction and a number of millennium-long climate model experiments are investigated for long-range memory (LRM). The models are two Earth system models and two atmosphere–ocean general circulation models. The periodogram, detrended fluctuation analysis and wavelet variance analysis are applied to examine scaling properties and to estimate a scaling exponent of the temperature records. A simple linear model for the climate response to external forcing is also applied to the reconstruction and the forced climate model runs, and then compared to unforced control runs to extract the LRM generated by internal dynamics of the climate system. The climate models show strong persistent scaling with power spectral densities of the form S(f) ~ f −β with 0.8 < β < 1 on timescales from years to several centuries. This is somewhat stronger persistence than found in the reconstruction (β &amp;approx; 0.7). We find no indication that LRM found in these model runs is induced by external forcing, which suggests that LRM on sub-decadal to century time scales in NH mean temperatures is a property of the internal dynamics of the climate system. Reconstructed and instrumental sea surface temperature records for a local site, Reykjanes Ridge, are also studied, showing that strong persistence is found also for local ocean temperature.

Highlights

IntroductionThe power spectral density (PSD) of long-range memory (LRM) time series follows a power law limf →0 S(f ) ∝ f −β , where β = 1 − γ and 0 < β < 1
The presence of long-range memory (LRM) in climatic records is well documented in the geophysics literature.LRM is characterized by an algebraically decaying autocorrelation function (ACF) limt→∞ C(t) ∝ t−γ such that ∞ 0 C (t )dt = ∞, i.e. 0 < γ ≤ 1.Equivalently, the power spectral density (PSD) of LRM time series follows a power law limf →0 S(f ) ∝ f −β, where β = 1 − γ and 0 < β < 1.A typical model for an LRM stochastic process is the persistent fractional Gaussian noise
The figures show (a) the temperature data, and (b) PSD, (c) DFA2, and (d) WVA2 applied to the data set

Summary

Introduction

The power spectral density (PSD) of LRM time series follows a power law limf →0 S(f ) ∝ f −β , where β = 1 − γ and 0 < β < 1. A typical model for an LRM stochastic process is the persistent fractional Gaussian noise (fGn). This is a stationary process with 0 < β < 1. The cumulative integral (or sum) of such a process has the PSD of the form S(f ) ∼ f −β , but with β → β+2. Such a process with 1 < β < 3 is a non-stationary

Methods

Results

Conclusion