Research article
Is the volatility and non-stationarity of the Atlantic Multidecadal Oscillation (AMO) changing?

https://doi.org/10.1016/j.gloplacha.2020.103160Get rights and content

Highlights

  • The GARCH model was developed for the AMO and its cold and warm phases.

  • The AMO shows a tendency toward more non-stationarity and volatility.

  • The cold phases show more volatility than the warm phases.

  • The non-linearity is increasing while the memory of the AMO is declining.

Abstract

Better understanding of the Atlantic Multidecadal Oscillation (AMO) temporal evolution and the precise and reliable predictability of its phase-switching behaviour are of utmost importance in characterizing future climate change as well as its consequences. For the first time, this study investigated internal dynamics of the AMO in different warm/cold phases to examine whether this phenomenon is governed by a non-linear process through time or not. Also, changes in heteroscedasticity of the AMO and its memory structure were explored using Generalized AutoRegressive Conditional Heteroscedasticity (GARCH) models. The developed GARCH models showed a high volatility or a rapid change of the heteroscedasticity of the AMO and its different phases while the memory in the variance regarding the conditional variance parameter was not significant except the first and last warm phases. Also, the volatility parameter showed very high increasing rate from 1875 to 2018. This implies that the fluctuation in the variance has been increasing and the memory in the AMO has been declining in recent decades. The test for stationarity revealed the tendency of increasing volatility in recent decades. The change in the conditional variance is exponentially increasing by the AMO values and the non-linearity has been clearly increasing in recent decades. This non-stationarity, volatility and nonlinearity surge may result in less predictability of the AMO behaviour/phase-switching pattern as well as less predictability of its consequences and effects on the global atmospheric and oceanic processes in future.

Introduction

The Atlantic Multidecadal Oscillation (AMO) is a low frequency large-scale mode of Sea Surface Temperature (SST) variability in the North Atlantic which exerts a wide range of profound impacts on climate subsystems and ecological dynamics on a global-scale (Sutton and Hodson, 2005; Knight et al., 2006; Chylek et al. (2014a); Drinkwater et al., 2014; Nye et al., 2014; Moore et al., 2017). This oscillating oceanic phenomenon is typically quantified by a spatially-weighted mean SST of the North Atlantic (0°–65°N), commonly referred to as the AMO index (Schlesinger and Ramankutty, 1994; Lin et al., 2019). The AMO exhibits a phase-switching (warming/cooling) behaviour with a periodicity of 60–80 years (Moore et al., 2017). There is a vast body of evidence on the AMO-associated impacts on the global climate system (Knight et al., 2006; Wyatt et al., 2012; Chylek et al. (2014a); Vaideanu et al., 2018; Moore et al., 2017; Gao et al., 2019), regional weather condition (Semenov et al., 2010; Chylek et al. (2014b); Zhang and Delworth, 2007, Luo et al., 2018a, Luo et al., 2018b; Ruprich-Robert et al., 2018; Sun et al., 2019; Gan et al., 2019), droughts (McCabe et al., 2004; Mo et al., 2009; Nigam et al., 2011; Oglesby et al., 2012; Jiang et al., 2019), precipitation and streamflow variability (Enfield et al., 2001; Knight et al., 2006; Curtis, 2008; García-García and Ummenhofer, 2015; Fan et al., 2019), hurricanes (Goldenberg et al., 2001; Knight et al., 2006; Zhang and Delworth, 2006; Klotzbach, 2011), key environmental parameters and ecological process (Hetzinger et al., 2008; Huss et al., 2010; Marullo et al., 2011; Edwards et al., 2013; Drinkwater et al., 2014; Nye et al., 2014; Alexander et al., 2014; Börgel et al., 2018; Wu et al., 2019; Lizcano-Sandoval et al., 2019), fisheries (Alheit et al., 2014; Faillettaz et al., 2019) and even the human health (Bonomo et al., 2019). Hence, a better understanding of the AMO dynamics in general, and more specifically of the AMO characteristics changes in different periods is of utmost importance.

Current discourses on physical nature, mechanisms, regime dynamics and internal variability of the AMO are rising (Lin et al., 2019). Several oceanic/atmospheric processes such as Atlantic Meridional Overturning Circulation (AMOC), random fluctuations in the atmospheric circulation, wind forcing, atmospheric blocking over the North Atlantic, anthropogenic global-scale warming and volcanic aerosols have been suggested as the driving and contributing forces to explain a part of the AMO variability (Drinkwater et al., 2014). Although different physical hypotheses have been proposed for the AMO variations, the exact underlying mechanism and detailed dynamics are still largely unknown and under debate (Lin et al., 2019).

In this paper, we do not intend to argue the (complex and unclear) physical mechanisms behind the AMO variability. Instead, we comparatively investigate the statistical characteristics and more specifically, the time-varying long and short memory structure/dynamics of the AMO index during the warming/cooling phases. Oscillations in the Atlantic Ocean such as the AMO and the North Atlantic Oscillation (NAO) and their dynamics have strong and large-scale influence on weather and climatic variations. There is ample evidence that demonstrate a strong connection between the AMO and the hemispheric meridional oscillation, the NAO (Delworth et al., 2017). These Oscillations are closely associated, in particular, with regional blocking and atmospheric memory and extremes (Luo et al., 2016; Luo et al., 2017). Better perception of internal variability of the AMO may help to provide more reliable and skilful forecasts on periodicity and switching dynamics of this phenomenon in the future. Also, the AMO-derived estimates are among the main model components in a number of decadal climate projection systems (Kavvada et al., 2013; Wei et al., 2017). Semenov et al. (2010) highlighted the potential significance of internal multidecadal variations in the “North Atlantic–Arctic sector” in driving long-term interdecadal regional, northern hemispheric and even global-scale climatic alterations. For instance, Luo et al. (2017) demonstrated that the recent AMO phase switching is a main reason of the recent cooling during the wintertime over the Eurasian region. Semenov et al., 2010also noted that the presence of internal variations in a climatic phenomenon is likely to complicate identification and detection of anthropogenic signals of climate change. These internal variations (if present and strong) in presence of only relatively moderate anthropogenic forcing could magnify changes in climatic conditions which might lead to extreme alterations in climate (Semenov et al., 2010).

The specific significance of recognition of the AMO temporal evolution and the precise and reliable predictability of its phase switch in characterizing future climatic changes, has been pointed by Ting et al. (2009). If the AMO warming phase continues (continuous upward trend), the SST in the North Atlantic may increase unprecedentedly (more rapidly than the global rate) and its potential combination with anthropogenic warming may intensify this alteration (see also, Allan and Allan, 2019). If the contemporary AMO trend begins to proceed to the opposite direction, the warming of the major part of the North Atlantic will lag other areas which will consequently impact the adjacent regions such as Mediterranean, north eastern North America as well as Western Europe (Ting et al., 2009). Therefore, modelling the temporal changes of the AMO is a crucial task for improving our knowledge on its evolution and its consequences in the future of climate dynamics. Time series models are the most common tool for investigating and modelling temporal behaviour of hydro-climatic variables. Time series models are usually classified as linear and non-linear models (Modarres and Ouarda, 2014) including the Autoregressive Moving Average (ARMA) and Generalized AutoRegressive Conditional Heteroscedasticity (GARCH), respectively.

The GARCH process (Engle, 2001) is an appropriate and promising tool to investigate the time-varying internal dynamics and change in memory structure in a given chronological data series. Unlike the most conventional time series analysis techniques, GARCH-type models are particularly capable of capturing non-linear characteristics (i.e. conditional variance or the second order moment) of hydro-climatic processes (Fathian et al., 2019). The GARCH models are mainly originated from studying the non-linear time-varying processes in econometrics but recently, there has been a growing tendency and interest in the application of these models in climate and hydro-meteorological time series studies (e.g. Mills, 2004; Wang et al., 2005; Modarres and Ouarda, 2013a, Modarres and Ouarda, 2013b). It should be noted that although the linearity in the mean or the first-moment of climatic data series can be easily captured by classic linear ARMA processes, the variance or the second-order moment of climatic variables that might be responsible for non-linearity, is not often explored in hydro-climatic time series such as the AMO index. There are little attentions by the climate researchers to test and model potential non-linearity in the AMO time series and especially to comparatively investigate that during warming/cooling phases.

This study mainly aims to have a new look at the AMO by examining whether it behaves in a non-linear manner. In addition, this study attempts to explore the changes in conditional variance (heteroscedasticity) of the AMO index and to characterize its memory structure during warming and cooling periods by applying a set of GARCH models. This might help to improve our understanding of the AMO future variability as well as its phase-switching dynamics. Hence, the main focus of this paper is on developing univariate non-linear GARCH processes which have not been employed for time series analysis of the AMO index yet (to the best of our knowledge).

Section snippets

Data

In this study, we used monthly time series of the AMO index (for the period January 1875 to December 2018) provided by NOAA's Earth System Research Laboratory (https://www.esrl.noaa.gov/psd/data/correlation/amon.us.long.data). The AMO index calculation is based on the monthly datasets of Kaplan SST averaged (area weighted) over the north Atlantic sector with subsequent linear trend removal. The exact duration of the warm (positive) and cold (negative) periods of the AMO as well as the timing of

Descriptive statistics

The descriptive statistics (Supplementary Table 1) show that the mean of the warm and cold phases have increased while the change is the mean of warm phases is stronger and has increased triple times in the PH5W than the PH1W. However, the (unconditional) variance does not show a significant change in recent decades which may imply that the range of AMO values has not changed significantly within different phases. Interestingly, regarding the maximum and minimum AMO values, it can be observed

Discussion and conclusion

To the best of our knowledge, the conditional variance and volatility of the AMO have not been investigated yet. However, other studies on the ENSO (Modarres and Ouarda, 2013a) and the NAO time series (Mills, 2004) have shown the variability and changes of the volatility and conditional variance in recent decades. In this study, the memory and stationarity of the AMO in different cold and warm phases were examined and reported for the first time.

The AMO indicates a strong memory in the mean, or

Recommendations for future studies

The future investigation on the AMO may go to the detailed characterizing the impact of time varying variance on the global oceanic and atmospheric interactions. As a strong and non-linear model, the GARCH model enables us to search for memory and its changes through time. As hurricane is one of the major harmful atmospheric/oceanic phenomenon which is influenced by the AMO variability, the next recommended steps is to investigate the volatility change of hurricane activities through time and

Data availability

The data supporting the findings of the present study are available within the manuscript and the appendix.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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