# Deconstructing Global Temperature Anomalies: An Hypothesis

## Abstract

**:**

_{2}), ENSO activity and tidal components, and indicate a causal sequence from tidal forcing to greenhouse gas (GHG) release to temperature increase. Tidal periodicities can all be expressed in terms of four fundamental frequencies. Because of the potential importance of this formulation, tests are urged using general circulation models.

## 1. Introduction

#### 1.1. Background

- (1)
- tidal forces from the sun and moon vary predictably;
- (2)
- these external tidal forces exist in alternately dominating meridional (approximately north–south) and zonal west–east) directions;
- (3)
- these tidal forces provide an exogenous driver of global ocean and atmospheric variability, on timescales from subdecadal to multidecadal, in a manner to some degree deterministic, predictable and testable; and
- (4)
- this exogenous forcing engenders decadal-scale slowdowns in global mean surface temperatures.

#### 1.2. The Tidal Hypothesis

_{1}+ 2f

_{2}− f

_{3}and so on. Adding and subtracting two frequencies (reciprocals of periods) generates two more frequencies. This process of frequency combination (sometimes called frequency demultiplication, e.g., [19]) has been invoked (for example) by Keeling and Whorf [20] and by two studies of the quasi-biennial oscillation to be described later. Such frequency combinations are a common feature of systems with interacting oscillators, as with intermodulation in electrical systems and vibration-rotation bands in spectroscopy. Treloar [21] chose an approach that has become accessible in recent decades. As the tidal potential depends on the distances and directions of the sun and moon in relation to the earth, the latter parameters can be computed from astronomical polynomial algorithms [22], which are reasonably accurate over several centuries. Using this source, and with a simple physical model reflecting the combined mass/distance

^{3}contributions from sun and moon, three-dimensional tidal forces varying over time were partitioned into components parallel and perpendicular to the plane of the moon’s orbit, approximately equivalent to zonal and meridional (or east–west and north–south) earth-based directions respectively. There is therefore a distinction between zonal and meridional tidal regimes in the understanding of the climate oscillations discussed here. Previous tidal approaches to the climate system have often focused on meridional forcing associated with the 18.6-year lunar nodal cycle. As developed, the formulation [21] identified the same, but found more prominent meridional components, and even more prominent zonal components. This study will suggest that the tidal components found in the earlier study, and others added in the present one, unlock many puzzles surrounding oscillations in the climate system. However, given the complexity of the topic and the simplicity of the physical model used, the hypothesis developed here is inevitably exploratory.

- describes the zonal or meridional characteristics of the components;
- explains the assumption that tidal periods are expected to be time-averaged;
- distinguishes between the treatment of the 18.60-year lunar nodal cycle in this and some previous studies of tidal forcing

#### 1.3. Upwelling and Ocean Temperatures

## 2. Materials and Methods

_{1}, ν

_{2}, ν

_{3}and ν

_{4}, correspond to the 59.75-, 86.81-, 186.0- and 5.778-year periodicities derived [21]; findings from this source are summarized and slightly updated in the Appendix A.

_{lag}$-\text{}\mathrm{t}$

_{0}]/P) or $\mathrm{cos}(2\mathsf{\pi}\mathsf{\nu}[\mathrm{t}\text{}+$ t

_{lag}$-\text{}\mathrm{t}$

_{0}]), where P is the component period in years, ν is the component frequency in reciprocal years, t

_{0}(as described in the Appendix A) is the component reference time or “date-stamp” (1918.20 or 2039.96), and t

_{lag}the time in decimal years that the climate response lags the tidal stimulus. For example, the correlation of SST data can be tested against the 18.60-year oscillation for an SST time lag of 0.1 years when SST data are expressed in the form: $\mathrm{cos}\text{}\left(2\mathsf{\pi}\left[\mathrm{t}\text{}+0.1-\text{}1918.20\right]/18.60\right)$, where t represents the decimal year corresponding to an SST data point, and so on for other pairs of tidal and climate oscillations.

## 3. Results

#### 3.1. Multidecadal Scale

_{0}of tidal extrema (maxima or minima) can be used to generate other corresponding times of extrema by adding or subtracting integer multiples of the cycle periods. For example, another maximum for the 86.81-year cycle occurs in 2039.96-86.81, and so on. The 59.75- and 86.795-year events listed in Tables I and II [21] can be generated by integer-multiple differences of the 59.75- and (now amended) 86.81-year periods from 2039.96. The t

_{0}parameter represents an effective “time-stamp” for each cyclic component, and the tidal hypothesis stands or falls if this timing is found to be incompatible with patterns in climate or ocean oscillations. This table also lists the “beating amplitudes” described in the Appendix A.

- (1)
- the 59.75-year zonal cycle minus the meridional 86.81-year cycle only, i.e., A59.75-A86.81;
- (2)
- 59.75-year cycle minus the sum of the meridional 86.81- and 186.0-year cycles, i.e., A59.75- (A86.81 + A186.0); and
- (3)
- the 59.75-year cycle minus the difference between the 86.81- and 186.0-year cycles, i.e., A59.75- (A86.81 − A186.0).

- (1)
- the ~60-year tidal oscillation, iterating its vertical scaling and displacement, and its lead time with respect to the GMST anomalies’ and
- (2)
- an exponential rise in background temperatures, iterating its asymptotic starting year, a multiplier for the exponential, and the exponent itself.

^{−6}; b = −0.37 °C; and with this Z-M difference accumulated after 1841.5. The series of accumulated tidal values from 1842.5 onward are reassigned such that values at decimal year t become values at t + 8, to co-vary with the eight-year lag in ~60-year global temperature oscillations;

^{d}where c = 5.2 × 10

^{−7}and d = 2.80

^{−6}, -0.37 °C, 5.2 × 10

^{−7}and 2.80, respectively.

^{−6}factors are multiples of the accumulated Z-M differences, producing the mean peak to valley ~60-year oscillation temperature range in Figure 3 of about 0.2 °C.

- (1)
- Oceanic processes can affect angular momenta and LOD. During El Niños, easterly winds along the equatorial Pacific decrease, which increases atmospheric angular momentum. However, the earth’s total angular momentum must stay constant, so the speed of rotation of the solid earth slows down, and LOD increases [50]. In addition, when evaporation or precipitation occurs over the oceans, mass is redistributed, producing changes in the earth’s atmospheric angular moment [51].
- (2)
- Atmospheric processes can affect angular momenta and LOD. The characteristic time for vertical transport of gases from the surface to the stratosphere is 5–10 years [52], and water vapor and carbon dioxide are present in atmospheric layers up to the stratosphere. Conceivably, evaporation and migration of these greenhouse gases from oceans to stratosphere occurs during the eight years’ lead time deduced above, during which the LOD and AAM change due to mass re-distribution, and global temperatures increase from the evolved greenhouse gases.
- (3)
- The evaporation process may be initiated by directional properties of tidal forcing. For example, a coupled model [53] simulated a significant increase in global AAM, the increase contributed by an acceleration of zonal mean zonal wind in the tropical-subtropical upper troposphere. Consistent with this, global temperatures increase most in zonal circulation regimes after 1844, 1903 and 1966 (Figure 3), in response to zonal tidal regimes that lead global mean surface temperatures by eight years.
- (4)
- The quasi-biennial oscillation (QBO) modulates the zonal mean wind and the mean meridional circulation, and induces in the tropics large-scale transport of chemical species into the stratosphere [40]. The relationship of tidal components to the QBO and the connection with tropical processes will be discussed in Section 3.3.

#### 3.2. Intermediate-Period Scale

_{0}following their formulation in the Appendix A.

_{lag}$-$ t

_{0}]/P). For example, testing a three-month lag time for GMST (or residual) data points at decimal years t in relation to the 14.94-year tidal cycle means testing the GMST data against the cosine relationship $\mathrm{cos}\left(2\mathsf{\pi}\left[\mathrm{t}+0.25-2039.96\right]\text{}/\text{}14.94\right).$

^{−2}and 1.3 × 10

^{−4}respectively; the multiple R was 0.68. The negative multipliers and t statistics imply that tidal maxima from the two components were accompanied by lower GMSTs, consistent with tidal forcing promoting ocean upwelling. The 18.60-year harmonic component made no significant contribution (p = 0.58).

_{5}+ ν

_{6}and ν

_{5}− ν

_{6}, therefore equivalently from ν

_{1}and ν

_{2}. Since the generating components had reference times t

_{0}at 2039.96, the new components are assumed to have the same t

_{0}. The period results were slightly corrected to means of 8.850 and 47.92 years by finding intervals from 2039.96 with frequent occurrences of close syzygy. In the case of the slightly irregular 8.850-year component, Fourmilab shows that every third interval occurs near alternately close new and moon events, but these close syzygy events are displaced from the 2039.96 reference time t

_{0}by half a cycle. Over many three-fold cycle intervals, the mean cycle period is 8.850 years. Despite the half-cycle displacements, when climate oscillations are compared with functions cos (2π[t + t

_{lag}− 2039.96]/P), the same t

_{lag}is found to apply to the 8.850-year component. It was unexpected to find the period (8.850 years) of the moon’s apsidal precession numerically generated by a combination of ν

_{5}and ν

_{6}, and equivalently of ν

_{1}and ν

_{2}, components. Other new components generated are 3.495- and 16.69-year components from ν

_{4}and ν

_{8}, so ultimately from ν

_{1}, ν

_{2}and ν

_{4}. Often, 3.5-, 5.8-, or ~17-year ocean cycles have been reported (e.g., [55,56,57]). As may be expected, higher frequency tidal components tend to show more significance in monthly than in annual datasets.

^{−7}(Year − 1850.5)

^{2.83}for the unsmoothed case; and

^{−7}(Year − 1850.5)

^{2.81}for the decadally smoothed case.

- (1)
- an exponential component that resembles models for the effects of greenhouse gas concentrations;
- (2)
- a ~60-year oscillation caused by an eight-year lagged response to exogenous multidecadal tidal forcing, possibly through the delayed temperature response from vertical transport to the atmosphere of greenhouse gases during zonal regimes;
- (3)
- intermediate-period temperature variability caused by decadal-scale tidal forcing, with different contributions during zonal and meridional regimes, and with temperature response lagging the tidal stimuli by 0.4 or 0.45 years (about five months); and
- (4)
- other contributions, not quantified in this paper, that may include those from episodic volcanic emissions and man-made emissions of pollutant aerosols.

#### 3.3. Short-Period Scale

#### 3.3.1. Unsmoothed Residual Anomalies, Lower Tropospheric Temperatures and CO_{2} Levels

_{2}datum − 0.02865(Year) + 55.408].

_{2}data and the two temperature datasets vary in near-synchrony. A causal relationship between evolved CO

_{2}and temperature might be argued either way, but the inter-connection seems undeniable.

_{2}annual increments is obtained with a lag of 0.24 years. Whether the lag time differences are meaningful is a topic for further study.

_{2}annual increments, unsmoothed GMST anomalies using a simulation with only three components. The results support a causal connection between the simultaneous increase of CO

_{2}and temperature on subdecadal timescales. The unsmoothed GMST anomalies and a three-component simulation derive from the present formulation of exogenous tidal forcing, this forcing appearing from Figure 8 to generate the simultaneous evolution of CO

_{2}and increase in temperature. The regression of unsmoothed residuals vs. the three tidal-component combination is not quite significant (p = 0.052), but the correlation is much higher in the zonal regime (p = 0.0065).

_{2}increments with those reflecting ENSO activity will be discussed in Section 4.1.

#### 3.3.2. The Quasi-Biennial Oscillation (QBO)

^{−}

^{38}and 3.3 × 10

^{−}

^{59}. Again, we find a strongly regime-dependent oscillation. The highest correlation with the combination of two tidal components is with a QBO lag time of 0.15 years (p = 9.0 × 10

^{−88}). A smaller but statistically important contributor to the meridional regime is the 3.495-year component (p = 9.7 × 10

^{−9}), whose contribution is omitted from Figure 9. In the Figure, maxima in the 2.213-year oscillation and QBO coincide around 1956; taken with the coincidences in the later meridional regime, this suggests a phase match over more than 25 cycles of the 2.213-year component, and consistent with a maximum near its 2039.96 reference time.

#### 3.3.3. The Oceanic Niño Index (ONI)

#### 3.3.4. The Atlantic Multidecadal Oscillation

- (1)
- a regression of F(t) against the AMO produces a p statistic of 2 × 10
^{−139}; and - (2)
- the amplitude of the F(t) function in the AMO is 0.047 °C, compared to the 0.02 °C amplitude for the ~60-year oscillation in GMST anomalies (Figure 3).

- (1)
- while analyses above for equatorial or global oscillations showed no statistical evidence of the 18.60-year tidal component, it is a significant contributor to the AMO;
- (2)
- the 180-year component correlation is significant during zonal and meridional regimes; and
- (3)
- these aspects may be consistent with the mid-latitude and meridional (in geographic terms) nature of the AMO.

^{18}O coral data (1751–2004) [62], Labrador algae (1365–2007) [63] and Nordic Sea ice (about 1600–1990, curve inverted) [64]. A comparison [62] showed some differences between the Puerto Rican δ

^{18}O coral proxy and more land-based AMO reconstructions by Gray et al. [65] and Mann et al. [66]. In relation to a marine oscillation (the AMO), a proxy from tidal forcing might correspond more closely with marine AMO proxies from coral, algae or sea ice. The tidal formulation may be a starting point for understanding these reconstructions, including the amplitude modulation noted [64] in longer-term AMO data.

#### 3.4. Summary and Comparison of the Degree to Which Tidal Components Contribute to, and May Ultimately Explain, Climate Oscillations.

_{2}oscillations on the bidecadal to subdecadal scale, presumably influencing both surface and sub-surface ocean circulation in different ways. Decadally smoothed GMST anomalies, LT temperatures and atmospheric concentrations of greenhouse gases (using CO

_{2}as an indicator) can be simulated by two to six intermediate-scale tidal components (Figure 5 and Figure 6). Subdecadal tidal components simulate GMST residual anomalies, detrended UAH LT temperatures and detrended annual CO

_{2}. The subdecadal Figure 8 shows minima and maxima similar to the timing of major ENSO events, suggesting that ENSO modulates greenhouse gas release from the oceans. In Figure 10, the ONI is moderately well simulated by the five subdecadal tidal components; the ONI is a standard for identifying major ENSO events. In Figure 9, a combination of the two shortest period tidal components closely simulate QBO 30mb zonal winds. In Figure 11, after removing a simulation of the ~60-year oscillation, the AMO is less well simulated by intermediate and short period components, but the 18,60-year component appears to contribute to the AMO, presumably because of its meridional and mid-latitude character.

## 4. Discussion

#### 4.1. General Comments

_{0}(2039.96). The multiples for ν

_{12}may be somewhat at odds with the others, but selection rules governing the choice of frequency multiples for this system are not known to this author. Apart from the eight-year lag time postulated with reference to slowdowns in global temperature anomalies, the decadally smoothed GMST residuals lag the tidal stimuli by about five months and the unsmoothed residuals and other unsmoothed oscillations examined lag the tidal stimuli in times ranging from less than three months down to about two weeks.

#### 4.2. Future Examination of the Tidal Hypothesis

## 5. Conclusions

## Appendix A

_{0}of 1918.20 for the $186.0/18.60$ pair and 2039.96 for the other components. Close syzygy events apparently occur frequently enough in the sequence of cycles to establish a significant response by the ocean/atmosphere system. Stepping back intervals from the reference extrema times over several centuries led to virtually insignificant amendments to the seven periods mentioned: 5.778, 86.81, 21.70, 186.0, 18.60, 59.75 and 14.94 years, respectively. The agreement of Fourmilab results with cycle periods in Treloar [18] supports the accuracy of the algorithm and beating procedures. While small differences exist between the derived tidal components and those established from other sources, the resulting components have the advantage of being calibrated from a single, independent source. The amended tidal periods are listed in Table 1, Table 2 and Table 3. In the present paper, these derived early tidal components are expanded in number by harmonic and frequency combination methods described in the text.

_{0}(the central amplitude) and H (the half band width at half maximum) are determined empirically from the fit to the beating events:

_{0}(1/π) H/((t − T + zP)

^{2}+ H

^{2})

_{0}and H were: For the 86.81-year cycle, 10,000 and 13; for the 186.0-year cycle, 4000 and 16; and for the 59.75-year cycle, 12,000 and 4.5.

_{0}and H parameters for the successive pairs are 10,000 and 13, 4000 and 16, and 12,000 and 4.5. The first two pairs are meridional, and the third pair is zonal. The figure displays “beating amplitudes” of 500, 160 and 1700, which, after testing other options, are used in the text as provisional measures of the respective component contributions.

**Figure A1.**Lorentzian envelopes of beating events in tidal forcing for: (

**A**) the 59.75-/14.94-year zonal pair; (

**B**) the 86.81-/21.70-year meridional pair; and (

**C**) the 186.0-/18.60-year meridional pair.

## Acknowledgments

_{2}annual increments, and to several anonymous referees for their invaluable counsel. This study was unfunded.

## Conflicts of Interest

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**Figure 1.**The accumulated balance over time of zonal minus meridional components in the Atmospheric Circulation Index (ACI), compared with the tidal zonal (59.75-year) minus meridional (86.81-year) differences. The tidal curve is vertically scaled to the ACI anomaly in Leonid Klyashtorin’s [4] zonal units.

**Figure 2.**The accumulated annual Z-M difference from 1500 to 2100 with an eight-year lag, and an analog incorporating the F(t) function.

**Figure 3.**Adding tidal and exponential components to simulate annual unsmoothed HadCRUT4 global mean surface temperature (GMST) anomalies, the curves projected to 2040.

**Figure 4.**The mean percent contribution of the exponential component to GMST anomalies on the multidecadal scale after removing a ~60-year tidal oscillation.

**Figure 5.**Residual HadCRUT4 decadally smoothed anomalies after removing a ~60-year oscillation and an exponential rise in temperature, compared with a sum of 21.70- and 14.94-year tidal components with anomalies lagging the tidal combination by 0.45 years. Residuals calculated from anomalies prone to “end effects” in the smoothing process are labeled “less accurate”.

**Figure 6.**The result of adding four regime-dependent components to the previous analysis, compared with residual HadCRUT4 decadally smoothed GMST anomaly residuals, and with anomalies lagging the tidal combination by 0.40 years. Residuals calculated from anomalies prone to “end effects” in the smoothing process are labeled “less accurate”.

**Figure 7.**Root mean square errors (RMSEs) in successive models for decadally smoothed HadCRUT4 anomalies.

**Figure 8.**The scaled temporal variation from 1979 to 2016 of the unsmoothed GMST residual anomalies, detrended UAH lower tropospheric temperatures, and detrended CO

_{2}annual increments and tidal analog. The latter three curves are vertically offset for clarity.

**Figure 9.**Comparison of the monthly QBO dataset with the vertically scaled 2.123- and 2.396-year tidal oscillations, with a QBO lag time of 0.15 years.

**Figure 10.**A comparison of the Oceanic Niño Index with a combination of five subdecadal tidal components.

**Figure 11.**A simulation of the AMO over the time segments: (

**A**) 1856–1940; and (

**B**) 1940–2016, after removing the ~60-year oscillation captured by F(t), and then smoothing with a 13-month running mean. These are compared with a tidal analog, for an AMO lag time of 0.04 years with respect to the tidal analog. The tidal components are listed in Table 13.

**Table 1.**The nature of multidecadal tidal components in this parameterization. Beating amplitudes for the multidecadal cycles are the respective heights of the envelopes shown in the Appendix A.

Period P, Years | Frequency Designation | Reference Time, t_{0} | Beating Amplitude |
---|---|---|---|

59.75 | ν_{1} | 2039.96 | 1700 |

86.81 | ν_{2} | 2039.96 | 500 |

186.0 | ν_{3} | 1918.20 | 160 |

**Table 2.**Intermediate-period (approximately bidecadal) tidal components derived from three fundamental frequency components that are applied to simulate decadally smoothed GMST residual anomalies.

Period P, Years | Frequency Combination | Reference Time, t_{0} |
---|---|---|

14.94 | ν_{5} = 4ν_{1} | 2039.96 |

21.70 | ν_{6} = 4ν_{2} | 2039.96 |

18.60 | ν_{7} = 10ν_{3} | 1918.20 |

**Table 3.**The 5.778-year component and additional components generated by frequency combination from Table 1 components. The latter four are generated from both zonal and meridional component frequencies.

Period P, Years | Frequency Combination | Reference Time, t_{0} |
---|---|---|

5.778 | ν_{4} | 2039.96 |

8.850 | ν_{8} = ν_{5} + ν_{6} = 4ν_{1} + 4ν_{2} | 2039.96 |

47.92 | ν_{9} = ν_{5} − ν_{6} = 4ν_{1} − 4ν_{2} | 2039.96 |

3.495 | ν_{10} = ν_{4} + ν_{8} = 4ν_{1} + 4ν_{2} + ν_{4} | 2039.96 |

16.69 | ν_{11} = ν_{4} − ν_{8} = 4ν_{1} + 4ν_{2} − ν_{4} | 2039.96 |

**Table 4.**Regime-dependent amplitudes for cosine functions for tidal components with a 0.40-year lead time in relation to the decadally smoothed GMST anomaly residuals, in the Figure 6 simulation. The amplitude A entries are in °C for each component, and are given for each period P by $\mathrm{Acos}\left(2\mathsf{\pi}\left[\mathrm{t}+0.4-2039.96\right]/\mathrm{P}\right)$ with t in decimal years.

Period P, Years | 21.70 | 14.94 | 8.850 | 47.92 | 16.69 | 5.778 |
---|---|---|---|---|---|---|

A (Zonal), °C | −0.04 | −0.01 | −0.01 | −0.005 | −0.015 | 0 |

A (Meridional), °C | −0.03 | −0.02 | 0.015 | −0.015 | −0.015 | 0.01 |

**Table 5.**Statistical results for succeeding models of simulating HadCRUT4 decadally smoothed GMST anomalies.

Components of Regression | Decadally Smoothed Case: R, RMSE (°C) |
---|---|

Model 1. A single exponential factor: 5.0 × 10 ^{−6} (t − 1850.5)^{2.82} − 0.34 | 0.957, 0.0800 |

Model 2. The sum of the exponential and the tidal ~60-year oscillation. | 0.988, 0.0418 |

Model 3. As #2, plus 2 tidal cycles. | 0.994, 0.0321 See Figure 5. |

Model 4. As #2, plus 6 regime-dependent tidal cycles. | 0.995, 0.0297 See Figure 6 and Table 4. |

Period P, Years | Frequency Designation | Reference Time, t_{0} |
---|---|---|

2.396 | ν_{12} = 4ν_{8} − 3ν_{2} = 16ν_{1} + 13ν_{2} | 2039.96 |

2.213 | ν_{13} = 4ν_{8} = 16ν_{1} + 16ν_{2} | 2039.96 |

**Table 7.**A simulation for tidal component cosine amplitudes (in °C) over the period 1959.5 to 2016.5. The amplitude A entries are in °C for each component, and are given for each period P by Acos(2π[t − 2039.96]/P) with t in decimal years.

Period P, Years | 2.213 | 2.396 | 3.495 |
---|---|---|---|

A (Zonal), °C | 0 | −0.03 | 0.08 |

A (Meridional), °C | −0.06 | 0 | 0 |

**Table 8.**Probability p statistics (N = 58) in pair-wise regressions with higher-frequency oscillations from 1959 to 2016. The tidal data are derived from the simulation in Table 7.

CO_{2} annual increments | 7.9 × 10^{−8} | |

3 tidal component simulation | 0.0012 | 0.0026 |

Unsmoothed GMST residual anomalies | CO_{2} annual increments |

**Table 9.**Probability p statistics (N = 38) in pair-wise regressions of UAH LT temperatures with oscillations from 1979 to 2016. The tidal data are derived from the simulation in Table 7.

Unsmoothed GMST residual anomalies | 3.3 × 10^{−1} |

CO_{2} annual increments | 2.3 × 10^{−6} |

3 tidal component simulation | 0.0020 |

**Table 10.**Amplitudes for the five subdecadal tidal components in a simulation of the ONI. The ONI lags the tidal components by 0.22 years.

Period, years | 2.213 | 2.396 | 3.495 | 5.778 | 8.850 |

A (Zonal), °C | −0.6 | 0.5 | 0.5 | 0.3 | 0 |

A (Meridional), °C | 0 | −0.4 | 0 | 0.4 | 0.4 |

**Table 11.**Regime differences for subdecadal tidal components in multiple linear regression statistics with the ONI, for a lag time of 0.22 years.

Period, Years | Zonal t | Zonal p | Meridional t | Meridional p |
---|---|---|---|---|

2.213 | −2.7 | 0.0076 | 1.2 | 0.25 |

2.396 | 3.8 | 0.00016 | −1.8 | 0.066 |

3.495 | 8.5 | 6.1 × 10^{−16} | 1.7 | 0.088 |

5.778 | 2.7 | 0.007 | 4.6 | 5.6 × 10^{−5} |

8.850 | −0.031 | 0.98 | 4.0 | 6.2 × 10^{−5} |

**Table 12.**Regime differences in multiple linear regression t and p statistics of subdecadal tidal components against monthly AMO data with lag 0.04 years and after removing the ~60-year oscillation with the F(t) function. Samples: N(zonal) = 954; N(meridional) = 978.

Period, Years | Zonal t | Zonal p | Meridional t | Meridional p |
---|---|---|---|---|

2.213 | 2.0 | 0.042 | 1.9 | 0.054 |

2.396 | −3.6 | 0.00031 | 3.6 | 0.00040 |

3.495 | 1.9 | 0.055 | 3.5 | 0.00044 |

5.778 | −1.2 | 0.25 | 2.8 | 0.0050 |

8.850 | 1.6 | 0.10 | 6.9 | 7.8 × 10^{−12} |

14.94 | −1.9 | 0.064 | 0.47 | 0.64 |

16.69 | −6.9 | 9.6 × 10^{−12} | 1.1 | 0.26 |

18.60 | −3.7 | 0.00026 | 4.6 | 5.6 × 10^{−6} |

21.70 | 0.50 | 0.62 | −2.0 | −0.044 |

**Table 13.**Regime-dependent component amplitudes A in a simulation of the AMO after removing a ~60-year oscillation. The AMO lags tidal components by 0.04 years.

Period, Years | 2.213 | 2.396 | 3.495 | 5.778 | 8.850 | 14.94 | 16.69 | 18.60 | 21.70 |

A (Zonal), °C | 0.02 | −0.03 | 0.03 | −0.01 | 0.01 | −0.02 | −0.06 | −0.05 | 0.00 |

A (Meridional), °C | 0.03 | 0.03 | 0.03 | 0.02 | 0.12 | 0.00 | 0.00 | 0.09 | −0.02 |

**Table 14.**Tidal frequency components in climate oscillations examined in this paper. The penultimate column lists the regime in which the components show greatest responses in the climate oscillations discussed.

Frequency Designation | Period, Years | Frequency Combination | Representation for ν_{1} ν_{2} ν_{3} ν_{4} | Main Active Regime | t_{0} (AD) |
---|---|---|---|---|---|

ν_{1} | 59.75 | ν_{1} | 1000 | Zonal | 2039.96 |

ν_{2} | 86.81 | ν_{2} | 0100 | Meridional | 2039.96 |

ν_{3} | 186.0 | ν_{3} | 0010 | Meridional | 1918.20 |

ν_{4} | 5.778 | ν_{4} | 0001 | Meridional | 2039.96 |

ν_{5} | 14.94 | 4ν_{1} | 4000 | Both | 2039.96 |

ν_{6} | 21.70 | 4ν_{2} | 0400 | Both | 2039.96 |

ν_{7} | 18.60 | 10ν_{3} | 00(10)0 | Meridional | 1918.20 |

ν_{8} | 8.850 | 4ν_{1} + 4ν_{2} | 4400 | Meridional | 2039.96 |

ν_{9} | 47.92 | 4ν_{1} − 4ν_{2} | 4-400 | Both | 2039.96 |

ν_{10} | 3.495 | 4ν_{1} + 4ν_{2} + ν_{4} | 4401 | Both | 2039.96 |

ν_{11} | 16.69 | 4ν_{1} + 4ν_{2} − ν_{4} | 440-1 | Zonal | 2039.96 |

ν_{12} | 2.396 | 16ν_{1} + 13ν_{2} | (16)(13)00 | Zonal | 2039.96 |

ν_{13} | 2.213 | 16ν_{1} + 16ν_{2} | (16)(16)00 | Meridional | 2039.96 |

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Treloar, N.C. Deconstructing Global Temperature Anomalies: An Hypothesis. *Climate* **2017**, *5*, 83.
https://doi.org/10.3390/cli5040083

**AMA Style**

Treloar NC. Deconstructing Global Temperature Anomalies: An Hypothesis. *Climate*. 2017; 5(4):83.
https://doi.org/10.3390/cli5040083

**Chicago/Turabian Style**

Treloar, Norman C. 2017. "Deconstructing Global Temperature Anomalies: An Hypothesis" *Climate* 5, no. 4: 83.
https://doi.org/10.3390/cli5040083