# The Hiatus in Global Warming and Interactions between the El Niño and the Pacific Decadal Oscillation: Comparing Observations and Modeling Results

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}emissions and other greenhouse gases, volcanic aerosol, etc., drives the model.

## 2. Materials

_{2}) emissions are observed values that are used as a driving force for the model, as well as volcanic eruptions [6]. The global-mean temperature anomaly (GTA) is used in the literature to identify particular events, like hiatus periods and “tie” points in the global temperature change history.

_{2}index measures CO

_{2}emissions in pG/year. It is one of the drivers of the model. Compared to CO

_{2}concentrations in the atmosphere, the multidecadal detrended pattern is shifted 2–3 years backward (not shown).

#### Tie Pints, or Dated Events

## 3. Methods

#### 3.1. Pretreatment of the Data

_{2}series because this series shows a clear progressive increase with time. The series are then normalized to unit standard deviation. Since the paired data are measured in different units, normalizing just brings the data on a common scale, and the regression coefficient (the β-coefficient) becomes numerically equal to the r-statistics.

#### 3.2. Quantifying Running Leading-Lagging Relation for Pairs of Variables

**v**

_{1}= (A1, A2, A3) and

**v**

_{2}= (B1, B2, B3) in an Excel spread sheet, the angle is calculated by pasting the following Excel expression into C2: = SIGN((A2 − A1)*(B3 − B2) − (B2 − B1)*(A3 − A2))*ACOS(((A2 − A1)*(A3 − A2) + (B2 − B1)*(B3 − B2))/(SQRT((A2 − A1)

^{2}+ (B2 − B1)

^{2})*SQRT((A3 − A2)

^{2}+ (B3 − B2)

^{2})))).

**v**

_{1}and

**v**

_{2}are two successive vectors, through 3 consecutive points in the phase plot.

_{pos}− N

_{neg})/(N

_{pos}+ N

_{neg})

#### 3.3. Auxiliary Methods

_{2}and the 3 observed pairs of the corresponding smoothed series. We then stacked the 6 series to see if there would be dominating cycles in the observed system assuming that non-dominating peaks in the PSD cancel out. The same procedure was made for the simulated series. Ordinary linear regressions (OLR) were calculated with the standard algorithm found in SigmaPlot© (San Jose, CA, USA). However, any standard methods could be used. Lastly, we calculated the running average slope (n = 10) for GTA, LOESS smoothed the series, f = 0.2, p = 2 and identified the hiatus periods as those with negative slopes or slopes less than 1/20 of the range in slopes.

## 4. Results

**A**. Regressions between pairs of observed series and pairs of simulated series. The observed and the simulated raw series for the El Niño and PDO are shown in Figure 1a,b. The multidecadal series obtained by smoothing the raw series (LOESS smoothed with f = 0.2 and p = 2) were shown as series superimposed on the raw series. The observed raw series and the observed multidecadal (low frequency) series for the El Niño and PDO correlate p < 0.05 (Table 1). The same occurred for the simulated raw and simulated multidecadal series for the El Niño and PDO, p < 0.001. However, the observed and the simulated raw and multidecadal (low frequency) series for El Niño and PDO did not correlate, p > 0.08.

**B**

**.**The leading-lagging relations between the El Niño and PDO. Figure 3a shows the observed raw, but detrended and normalized, time series for the El Niño and PDO and Figure 3b the corresponding modelled time series. The LL-relations between the El Niño and PDO are shown in Figure 3c (observed) and 3d (simulated). Grey bars represent LL-relations so that a positive bar shows that the El Niño leads PDO and a negative bar shows that the El Niño lags PDO. A smoothed line characterizes the main pattern for LL-relations. The dashed lines denote confidence limits. The figure shows that El Niño is an overall leading variable to PDO, but there are periods where the LL-strength is weak, or opposite. Figure 3d shows the corresponding LL-relations found for the simulated pair of El Niño and PDO. The El Niño is a more persistent leading variable to PDO in the simulated series than in the observed series. For both the observed and the simulated pairs, the El Niño appears to be a less strong leader to PDO around 1910, 1960 and 2000. These years correspond approximately to hiatus periods (grey horizontal bars) but only to some years designated as regime shifts (black squares). However, a regression between the observed and simulated LL-strength series is non-significant, p > 0.1.

**C**. Power spectral density of LL-relations. The LL-series shifted several times between being leading and lagging during the period from 1861 to 2005, we also applied PSD analysis to the LL-relations (Figure 5a,b). Since we wanted to characterize the teleconnections system, we stacked all PSD plots to see if some cycle lengths would reinforce each other, while others would annihilate each other. The peaks in the PSD for the stacked observed LL-relations are shown in Table 2, row I. The PSD showed major peaks at 5, 11 and 13 years. The PSD for the stacked, simulated LL-relations showed major peaks at 5, 11 and 16 years. Both PSDs also showed minor peaks around 26 and 31 years (not shown in the PSD graphs).

**D**. Power spectral densities for single series. We show the power spectral series both as raw data and smoothed, to emphasize major features. For the single series we included cycle lengths up to 80 years because Minobe [10] suggests that there might be 50 to 70 year cycles over the North Pacific, Figure 5c and d. However, our time series are too short so that results for longer cycles would only be suggestive. We therefore report cycle length results for the short range (0–32 years) and the long range (33–70 years) separately. There are peaks at similar cycle length in both the observed and the simulated data. In the short cycle length range, we found a cycle length of 21 and 31 years for the observed El Niño and 11 and 32 years for the simulated El Niño. For the observed PDO we found cycle lengths of 8, 22 and 28 years and for the simulated PDO at 7, 11, 20 and 31 years. In the long cycle range, 33 years and above, we found similar cycles for the two time series around 44–49, 62 and 70–72 years , Table 2, Row II and III.

**E**. Cycle lengths for paired time series. With the partial ellipse method, we estimated the common cycle length by averaging cycle lengths. For the observed variables, we found 7.9 ± 2.5 years for the raw series and 24.5 ± 3.2 years for the smoothed series, Figure 3e and Figure 4e. Corresponding estimates for the simulated variables were 8.4 ± 4 years and 23.9 ± 3.0 years, Figure 3f and Figure 4f. The cycle length for the observed and the smoothed series was in no cases statistically different.

**F**. Phase shift. The values for phase shifts were 1.18 ± 0.5 years, 1.19 ± 0.53 years for the raw observed and simulated data, 4.6 ± 4.7 years, and 4.9 ± 4.6 years for the smoothed observed and simulated data.

## 5. Discussion

_{2}emissions), we also suggest years when observations or simulations, or both, indicate particular events.

#### 5.1. Raw and Smoothed Time Series

#### 5.2. Paired Series

**A.**Regressions. A linear regression between the El Niño and PDO shows a significant correlation both in the observed set and in the simulated one. Since the model is partly driven by observed forcing, like CO

_{2}emissions, trends and deviations from the trends in the driving forces may be reproduced in the simulated values. However, the simulated and the observed series for both El Niño and PDO did not correlate p > 0.1. Thus, even though both El Niño and PDO visually show common characteristics, the OLS did not capture their similarity as significant. However, shifting one series relative to the other may improve correlation. The LL-technique discussed below addresses this cross-correlation issue.

**B**. LL-relations. When we say that one series leads another, the interpretation is that peaks (or troughs) in the leading series are in front of peaks (or troughs) in the target series and closer than ½ of their common cycle length, (λ). However, very long leading times may occur that exceed ½ λ. Secondly, two series that show LL-signatures may be driven by a third series, but with phase shifts relative to this series. Using the leading series for prediction is still possible, but the leading series need not have a causal effect on the second series. The latter is common in biological systems where one species reacts slower to, for example, warming than another [29].

**C**. The power spectral density for LL-relations (El Niño, PDO and CO

_{2}series), shows that the cycle length is similar for the observed and the simulated series. Both show major peaks at 5 and 11 years, (Figure 5a,b). In the simulated variables, there is also a pronounced 16 years cycle. Both series also show peaks at 26 and 31 years (not shown in graphs). The peaks suggest that there are cycles in the LL-strength, but the results in Figure 3c,d show that the PDO is a leading variable to El Niño only two or three times during our 140-year study period. Since these events occur very closely at the same time both in the observations and in the simulations, it should be possible to identify almost exactly why these events occur.

**D.**Power spectral density for the single series. Since spectra for six paired series (El Niño, PDO, CO

_{2}, raw versions and LOESS smoothed) show common characteristics, we compared superimposed spectra from the observed series to superimposed spectra based on the random series (not shown). We conclude that the spectra based on observed and simulated time series represent real signals because peaks stand out more clearly in the PSD graphs based on the observed series than on those based on the random series. We have not developed a significance test for this case. Our results on the short cycle lengths showed that the El Niño did not have a marked peak below 11 years, but there were several smaller peaks. Our results on the long cycle lengths > 32 years suggest that distinct long cycles exist, but the time series used are too short to establish such cycles with certainty.

**E.**Common cycle lengths. The cycle length found with the partial ellipse method was 7.9 ± 2.5 years based on the raw series and 24.5 ± 3.2 years based on the smoothed series.

**F**. Phase shift. Phase shifts are normally found by cross correlation, and the results with the LL-method can be compared to results by this method. Covariances between El Niño, PDO and CO

_{2}are observed by Patra, Maksyutov [35]. The shift between the time series are about ¼ of a cycle length both for the short cycle length of the high frequency series and the long cycle length of the low frequency series suggesting that the El Niño and PDO will appear as orthogonal in PCA plots as shown by Wills, Schneider [9].

#### 5.3. Comparing Observations and Simulations

_{2}emissions were used as an exogenous driving force in the model and changes in the atmosphere CO

_{2}concentrations may change global warming system, including ocean circulations. Several authors also assign a role to volcanic eruptions and the subsequent albedo effects. For example, Mehta et al. [36] lists four major, low latitude volcanic eruptions that are associated with phase transitions in the PDO. Reid, Hari [4] attribute the global impacts in 1980 partly to the recovery from the El Chichón volcanic eruption in 1982 and Stevenson, Otto-Bliesner [15] suggest that both Northern and Tropical eruptions favor El Niño initiations. If there are triggering events, like volcanic eruptions, that ultimately cause hiatus periods, then their occurrence cannot be predicted. However, it should not be possible to associate the hiatus periods with other events than volcanic eruptions, but ocean interactions also appear to play a role.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Observed and simulated values for the El Niño and the Pacific decadal oscillation (PDO). (

**a**) Observed value and smoothed values. (

**b**) Simulated values; raw and smoothed values.

**Figure 2.**Relation between time series and phase plot. (

**a**) Time series: The candidate cause (CC) peaks before, and close to the target (T). They could represent sun insolation (cause) and sea surface temperature, (SST), respectively. (

**b**) Phase plot for CC and T (target, T, in x-axis). Note that for perfect sine functions centered and normalized to unit standard deviation the phase portrait will be an ellipse with center at the origin and the long axis along the 1:1 or the 1:−1 direction. (

**c**) Upper part: time series based on random numbers drawn from a uniform distribution; lower part: running angles. (

**d**) Phase plot for the time series in c. Points on the trajectories are numbered consecutively. Notice that the first angle 0-1-2 is positive (rotate counter clockwise). The angle θ is measured by Equation (2) in the main text. When ∑ θ ≈ 2π, a circle-like curve is closed and the number of time steps used to close the curve corresponds to the common cycle time of the two contributing time series. The Figure is redrawn after Seip and Grøn [23].

**Figure 3.**Leading-lagging relations between El Niño and PDO. (

**a**) Observed values including GTA slope; (

**b**) Simulation results; (

**c**) LL-relations for observed values. Grey bars show positive and negative rotations as angles. The line shows smoothed observations. The dashed lines show confidence estimates. Black squares represent regime shifts, grey horizontal bars indicate hiatus periods. Lower line centered at −4 shows running average slope, S, (n = 9) for Ang(El Niño, PDO) = s × El Niño; (

**d**) LL-relations, simulated values; Other legends as in figure c; (

**e**) Cycle length and phase shift, observed values; (

**f**) Cycle length and phase shift, simulated values. Other legends as in figure e.

**Figure 4.**Leading-lagging relations between smoothed El Niño and PDO. (

**a**) Observed values; (

**b**) Simulation results; (

**c**) LL-relations for observed values. The grey bars show positive and negative rotations as angles. The line shows smoothed observations. Dashed lines show confidence estimates. Black squares represent regime shifts, grey horizontal bars indicate hiatus periods, The lower line centered at −4 shows running average slope, s (n = 9) for Ang(El Niño, PDO) = s × El Niño; (

**d**) LL-relations, simulated values. Other legends as in figure (

**c**); (

**e**) Cycle length and phase shift, observed values, (

**f**) Cycle length and phase shift, simulated values. Other legends as in figure (

**e**).

**Figure 5.**Power spectral density (PSD) for observed and simulated data (

**a**) PSD graphs for LL-relations between observed variables El Niño, PDO and the CO

_{2}. Major peaks at 5, 11, 13 years. Minor peaks at 26 and 31 years. The peak at 13 years has a large contribution from the observed interaction between CO

_{2}and PDO (raw data); (

**b**) PSD for leading-lagging relations between simulated variables El Niño, PDO and CO

_{2}. Major peaks at 5, 11, and 18 years. Minor peaks at 26, 30 and 32 years. C = CO

_{2}; N = El Niño; P = Pacific decadal oscillation, S = simulated; R = raw and L = LOESS smoothed. The blue shades suggest the position of broad peaks in cycle length. (

**c**) PSD for El Niño. The observed series have peaks at 21, 31, 44 and 72 years. The simulated series has peaks at 11, 32, 48, 62 and 72 years, (

**d**) PSD for PDO. The observed series has peaks at 8, 22, 28, 46 and 70 years. The simulated series has peaks at 7, 11, 20, 31, 49, 62 and 72 years.

**Table 1.**Regression results for El Niño and PDO. n = 145 and regression results for Leading-lagging relations and global-mean temperature anomaly (GTA) slope, n = 62–73, LL(N,P) obtains a high value when El Niño leads PDO.

Variables | Raw Dta, High Frequency | Smoothed Data, Low Frequency | ||
---|---|---|---|---|

Regression, r^{2} | p | Regression, r^{2} | p | |

El Niño, Obs, PDO, Obs | 0.518 | <0.001 | 0.208 | 0.012 |

El Niño, Sim, PDO, Sim | 0.392 | <0.001 | 0.452 | <0.001 |

El Niño, Obs, El Niño sim. | 0.147 | 0.08 | 0.001 | 0.987 |

PDO, Obs, PDO sim. | 0.071 | 0.40 | 0.005 | 0.676 |

LL(N,P) obs GTAslope 21–93 | 0.024 | 0.21 | 0.090 | 0.01 |

LL(N,P)Sim GTAslope 21–93 | 0.424 | <0.001 | 0.452 | <0.001 |

**Table 2.**Cycle lengths. Row I: LL-relations, LL(El Niño, PDO) analyzed with power spectral density, PSD. Rows II, III: single series analyzed with PSD; Row IV: paired series El Niño, PDO with partial ellipse method.

Rows | Variable | Observed/Simulated | Cycle Length, Years | ||||||
---|---|---|---|---|---|---|---|---|---|

1st | 2nd | 3rd | 4th | 5th | 6th | 7th | |||

I | LL(El Niño, PDO) | Obs. | 5 | 11, 13 | 26 | 31 | |||

Sim. | 5 | 11, 16 | 26 | 31 | |||||

II | El Niño | Obs. | 21 | 31 | 44 | 72 | |||

Sim. | 11 | 32 | 48 | 62 | 72 | ||||

III | PDO | Obs. | 8 | 22 | 28 | 46 | 70 | ||

Sim. | 7 | 11 | 20 | 31 | 49 | 62 | 72 | ||

IV | El Nño-PDO | Obs. | 7.9 ± 2.5 | 24.5 ± 3.2 | |||||

Sim. | 8.4 ± 4.0 | 23.9±3.0 |

**Table 3.**Overview of the comparison criteria for the simulated and observed results. Similarities = visual similarity, but not significant. Clues to dates or mechanisms = there are years that appear distinct and that could give clues to mechanisms.

No. | Criteria | Significant/Similarities | Clues | Figure/Table |
---|---|---|---|---|

A | Regressions between pairs in observations and simulations | Observed El Niño and PDO are similar as is the simulated pair, Observed and simulated El Niño are different, as is the PDO pair. | Tie points may realign time series | Table 1 |

B | LL-relations, time series | El Niño and PDO LL-relations have common traits, but are not significantly correlated | Similar features in 1910, 1960, 2000 | Figure 2c,d Figure 3c,d |

C | Power spectral density, LL-relations | Peak at 5 and 13 years strongest in observation, peak at 11 years strongest in simulation | Unimodal and bimodal patterns, c.f. (1) | Figure 4c,d |

D | Power spectral density- single series | Peak at 31 years in observed and simulated El Niño; peak at ≈ 7 years and ≈ 28–31 years in observed and simulated PDO | Longer cycle lengths may exist | Figure 5c,d |

E | Common cycle lengths: Time series | Raw series are similar ≈ 8 years. Smoothed series are similar ≈ 24 years. | Longer cycle lengths may exist. | Figure 3e,f Figure 4e,f |

F | Phase shifts: time series | Raw series show similar phase shifts, ≈ 1 year; smoothed series show similar phase shift ≈ 5 years. | Longer phase shifts exist. | Figure 3e,f Figure 4e,f |

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**MDPI and ACS Style**

Seip, K.L.; Wang, H. The Hiatus in Global Warming and Interactions between the El Niño and the Pacific Decadal Oscillation: Comparing Observations and Modeling Results. *Climate* **2018**, *6*, 72.
https://doi.org/10.3390/cli6030072

**AMA Style**

Seip KL, Wang H. The Hiatus in Global Warming and Interactions between the El Niño and the Pacific Decadal Oscillation: Comparing Observations and Modeling Results. *Climate*. 2018; 6(3):72.
https://doi.org/10.3390/cli6030072

**Chicago/Turabian Style**

Seip, Knut L., and Hui Wang. 2018. "The Hiatus in Global Warming and Interactions between the El Niño and the Pacific Decadal Oscillation: Comparing Observations and Modeling Results" *Climate* 6, no. 3: 72.
https://doi.org/10.3390/cli6030072