_{1}

We report that the Atlantic Multi-Decadal Oscillation (AMO) shows the same phase-locked states of period 2 and 3 years that have been reported in many other climate indices. In addition, we find that the report by Muller, Curry et al. of an oscillation in the AMO of 9.1 years is a misinterpretation of a maximum in the Fourier spectrum.

The AMO index is the area weighted average sea surface temperature (SST) of the Atlantic Ocean from latitudes 0N to 70N. The multi-decadal oscillation period is reported as 65 - 70 years by Schlesinger et al. [

Studies of the AMO on decadal time scales are few. Douglass [

In this paper we will point out that we already know that the AMO has abrupt climate shifts [

We summarize results of prior investigations that will be discussed in this paper.

Abrupt shifts in various climate indices have been well documented. Trenberth [

Simultaneous climate shifts have been reported in a “global” set of indices [

• SST3.4, central tropical Pacific SST;

• NPC1 (PDO), Pacific Ocean between 20N and 65N;

• SPC1, southern Pacific SST; and

• AMO, the subject of this paper.

The climate shifts since 1950 are found to occur during the following years [

• 1956-1959;

• 1964-66;

• 1969;

• 1976-77;

• 1986-87 and

• 2001-02.

Weaker shifts were found at other dates. This list is consistent with climate shifts reported in prior papers.

A question arises: From what to what does the climate shift refer? The answer is: from one phase-locked state to another phase- locked state. See next section.

Phase-locked states in the Earth’s atmosphere/ocean climate system have been reported by Douglass [

This scheme is called the autocorrelation method (AM) in which the autocorrelation of the time segment containing the 2- or 3-year oscillations was calculated vs. the delay time τ. If this time segment contains a sinusoidal signal of period 2 or 3 years then the autocorrelation function will have a maximum at a delay of 24 or 36 months. See [

In a later paper Douglass [

• SOI, the Southern Oscillation Index;

• MSU-lt, equatorial lower troposphere temperature;

• PDO, the Pacific Decadal Oscillation (29N to 65N); and

• W3, an equatorial wind index.

All showed phase-locked states over nearly the same date ranges as SST3.4.

Douglass, Knox, Curtis, Giese and Ray [

AMO

The AMO index data are monthly values of the area weighted sea surface temperature (SST) of the Atlantic Ocean from the equator to 70N. The data range from 1856 to the present. We use the unsmoothed data set that can be downloaded at NOAA/AMO [

SST3.4

We also use the monthly values of El Ñino/La Nina index, SST3.4, for comparison. This data is the same that was used to defined and find 40 historical El Ñino episodes. See [

The data in both sets are measured in degrees Centigrade.

The first task is to remove the strong annual signal from the AMO. A very common method used to “remove” the annual signal is the “climatology” scheme. However, this scheme can lead to false signals in the derived anomaly index [

A M O _12 . (1)

As in [

h A M O = A M O − A M O _12 (2)

magnitude of the positive cycle is larger than the magnitude of the negative cycle means that there is a harmonic component.

After the annual signal has been removed one sees that there is a multi-centennial trend that must be removed before an anomaly index can be defined. At this point in the analysis of AMO_12 many investigators consider the global warming hypotheses as part of the trend and propose ways to model it. Some use a linear trend which is seen not to describe the trend. There is, in fact, no need to explain the trend. Just remove it imperially. Along with aAMO _12 (red) in

We define the AMO anomaly as

a A M O = A M O _12 − p o l y n o m i a l (3)

• 1863 to 1901;

• 1927 to 1965;

• 1997 to ? (see discussion below on this value).

These values are listed in

What is the value of the multi-decadal period?

WRM Time Intervals | |||
---|---|---|---|

begin | end | ||

1 | This paper | 1863 | 1901 |

Klotzbach et al. [ | 1878 | 1899 | |

2 | This paper | 1927 | 1965 |

Klottzbach | 1926 | 1959 | |

3 | This paper | 1997 | 2030-2035 |

Klotznach | 1995 | 2012 |

years. This new estimate is close to the value of 65 - 70 years given by [

When does the third warm time interval end?

Using the 68 - 72-year value for the period then adding it to the end of warm segment 2, the estimate for the end of segment 3 is 2030 - 2034.

Some have suggested that the third warm time segment has already ended [

Here we do not need to use anomalies to determine phase-locked states. We compare AMO_12 to the previously published results on SST3.4 [

The AMO_12 data were also analyzed by the autocorrelation method. When the beginning date was about April 1992 and the ending date was about April 2002 the plot in

One sees that there are 3 maxima in AMO_12 that occur after the 3 maxima of SST3.4_12. The lags are: 7, 0 and 12 months, respectively.

From Figures 3(a)-(c) one sees that each maximum in SST_12 is followed by a maximum in AMO_12.

We also calculated a delayed correlation plot of aAMO_12 vs. aSST3.4_12 from 1950 to 2016 (not shown). We found a maximum in the correlation coefficient of 0.77 when the aAMO_12 delay was 11 months. The associated relationship can be quantified as follows:

a A M O _ 12 = 0.1103 ∗ a S S T 3.4 _ 12 + 0.11 .

One sees that decadal changes in aAMO_12 are about 10 times smaller than changes in aSST3.4_12. Thus, these two methods of estimating delay are consistent with each other.

Muller, Curry et al. [

1) A high correlation of SST3.4 and AMO with AMO lagging by a few months.

SST3.4_12 | AMO_12 | |||||
---|---|---|---|---|---|---|

Seg | Range | State* n parity s | El ñino episode | Date of max | Date of max | Difference (months) |

9 | Jun 91 to Jan 99 | 3 ortho 0 | 32 | Jan 82 | Jul 93 | 17 |

33 | Oct 94 | Jul 95 | 11 | |||

`34 | Nov 07 | Aug 98 | 11 | |||

10 | Jan 01 to Mar 08 | 2 ortho 0 | 35 | Dec 02 | Sep 03 | 9 |

36 | Jan 05 | Jul 05-Jul 06 | 12 | |||

37 | Nov 06 | Jun 08 | 14 | |||

11 | Mar 09 to ? | 3 ortho 0 | 38 | Dec 09 | Jul 10 | 7 |

39 | Nov 12 | Nov 12 | 0 | |||

40 | Nov 15 | Nov 16 | 12 | |||

41 | Nov 18 | |||||

Average = 11 +/− 5 |

2) A claim of a strong signal in AMO of a period of 9.1 ± 0.4 years.

MC2013 show a plot of spectral power vs. the frequency in cycles/year for AMO. This plot has a narrow maximum at about 0.11 cycles/year (9.1 years) and a second and third maxima but are slightly smaller maximum at about 0.28 and 0.34 cycles/year (3.5 and 2.9 years), which we will label maxima 1, 2 and 3. We will call this combination of three maxima the “signature”.

1) Our result of AMO lagging SST3.4 by 11±5 months is consistent with the findings of MC2013.

2) Since our more detailed study of AMO found no signal of period 9.1 years we did a Fourier analysis of AMO. We calculated the Fourier spectrum of AMO using a fast Fourier transform (FFT) and obtained a plot with the same signature as reported by MC2013 and with the same 3 maxima. Thus, we agree. What is the explanation? While it is true that a periodic signal will result in a maximum in the Fourier spectrum the converse may not be true. In this case there is no 9.1 year periodic signal in AMO corresponding to the maximum in the Fourier spectrum. Also, if there were a signal of 9.1 years in ZMO there would be a maximum in the delayed autocorrecting function at a delay of 9.1 years. We calculated the autocorrelation function of AMO from 1950 to 2017 (the same range as in MC2013). We obtained a plot (not shown) almost the same as in

We conclude that the claim of MC2013 of a 9.1 year periodic signal is an error in interpretation of a maximum in the Fourier spectrum of AMO.

We have measured the AMO multi-decadal period to be 68 - 72 years which is close to the value of 65 to 70 years found in the literature. We also estimate that the present “warm” time interval will not end until about 2031/2035.

More importantly, we find that the AMO has time segments showing the same phase-locked states of periods 2 and 3 years as reported in many other climate indices. However, the AMO lags the SST3.4 by about a year.

In addition, we conclude that interpreting a maximum in the Fourier spectrum of AMO as an oscillation in AMO of period of 9.1 years is incorrect.

We wish to acknowledge helpful comments from P Klotzbach and R.S. Knox.

Douglass, D.H. (2018) Observation of Phase-Locked States in the Atlantic Multi-Decadal Oscillation (AMO). Atmospheric and Climate Sciences, 8, 344-354. https://doi.org/10.4236/acs.2018.83023