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On the spectral characteristics of the Atlantic multidecadal variability in an ensemble of multi-century simulations

Abstract

The Atlantic multidecadal variability (AMV) is a coherent pattern of variability of the North Atlantic sea surface temperature field affecting several components of the climate system in the Atlantic region and the surrounding areas. The relatively short observational record severely limits our understanding of the physical mechanisms leading to the AMV. The present study shows that the spatial and temporal characteristics of the AMV, as assessed from the historical records, should also be considered as highly uncertain. Using 11 multi-century preindustrial climate simulations from the Coupled Model Intercomparison Project Phase 5 (CMIP5) database, we show that the AMV characteristics are not constant along the simulation when assessed from different 200-year-long periods to match the observed period length. An objective method is proposed to test whether the variations of the AMV characteristics are consistent with stochastic internal variability. For 7 out of the 11 models analysed, the results indicate a non-stationary behaviour for the AMV time series. However, the possibility that the non-stationarity arises from sampling errors can be excluded with high confidence only for one of the 7 models. Therefore, longer time series are needed to robustly assess the AMV characteristics. In addition to any changes imposed to the AMV by external forcings, the detected dependence on the time interval identified in most models suggests that the character of the observed AMV may undergo significant changes in the future.

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Correspondence to Irene Mavilia.

Appendix

Appendix

A detailed explanation of the method for testing AMV stationarity

A detailed explanation of the method for testing AMV stationarity is given here using the MPI-ESM-P model example. The starting point is the generation of 1000 synthetic time series with the same length and the same spectrum as the model NASST time series (1156 years for the MPI-ESM-P model). In Fig. 9, the 1000 synthetic time series, in green, share the same spectrum (top plot) and autocorrelation (bottom plot) as the model time series (superimposed as a thick black line). Having verified this, it is possible to compute the 90% central range for the autocovariance function that represents the 90% range of variation of autocovariance values for each lag. Each of the 1000 synthetic AMV time series is split in 200-year-long intervals shifted by 1 year, obtaining 956(= 1156 − 200) intervals for MPI-ESM-P model. Therefore, there are 956,000 intervals for all the 1000 synthetic time series. The autocovariance function is computed for all these intervals, spanning 60 lags. For each lag, the 90% central range (i.e. the range between the 5th percentile and the 95th percentile) of the 956,000 autocovariance values is computed.

Fig. 9
figure9

(Top) model NASST spectrum in black and 1000 spectra associated to the 1000 synthetic NASST time series in green lines, via multi-taper method. (Bottom) model AMV autocorrelation in black and 1000 autocorrelations associated to the 1000 synthetic AMV time series in green lines

In parallel, also the model AMV time series is divided in 956 intervals and the autocovariance is computed for all of them. For each lag, the 956 autocovariance values are compared with the inferior and superior limits of the 90% central range and we count how many values exceed the range.

In order to have a reasonable number of intervals to be shown together, in Fig. 10 we plot the intervals shifted by 50 years instead of 1 year. Each plot refers to a different interval, the black line is the model autocovariance function for that interval, the grey shading is the 90% central range and the red curve represents the mean behaviour of the model intervals. Even from a visual inspection is possible to find periods where the autocovariance function falls outside the 90% central range (grey shading), showing that they do not have the same statistical characteristics as the whole time series. A more rigorous approach consists in counting the number of autocovariance values that fall outside the confidence interval. Taking into account all of the 956 intervals, there are 57,360 values (that is 956 intervals multiplied by 60 lags) in total. The result shows 8088 values outside, which corresponds to 14.1% of the total, meaning that, for the MPI-ESM-P model, 14.1% of the total amount of values fall outside the shading, as represented in Fig. 7 (blue triangle).

Fig. 10
figure10

Autocovariances for the 10-year low-pass filtered AMV time series split in 200-year-long intervals shifted by 50 years (black thick lines). The grey shading and the red curve are the same in all panels: the grey shading indicates the 90% central range of the autocovariance values for the entire time series and the red curve represents the average of the model autocovariance functions of the panels

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Mavilia, I., Bellucci, A., J. Athanasiadis, P. et al. On the spectral characteristics of the Atlantic multidecadal variability in an ensemble of multi-century simulations. Clim Dyn 51, 3507–3520 (2018). https://doi.org/10.1007/s00382-018-4093-7

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Keywords

  • Atlantic Multidecadal Variability (AMV)
  • Coupled Model Intercomparison Project Phase 5 (CMIP5)
  • Time Series
  • North Atlantic SSTs
  • Autocovariance Values