Hadcrut4 Analysis Essay

Don't panic when your instructor tells you that you need to write an analysis!  All he or she wants is for you to take something apart to see HOW it works.

To write an analysis, you need to think about how each part of something contributes to the success of the whole.

Caution!  Make sure that you're NOT just summarizing the original article, story, novel, poem, etc.  Go beyond simply telling us WHAT you are talking about: describe HOW and WHY its elements function.

Specific Information for Analyzing Literature

Summarizing = WHAT
Analyzing = HOW & WHY

When you think about analysis, try thinking about how you might analyze a car.

  • Ask yourself: What do we want the car to do or accomplish?
    • Answer: (minivan) “provide transportation for my family”
      • Analysis: how does each part of the van achieve this goal?
        • Example: gasoline powers the engine
    • Answer: (sports car) “speed, agility, and style”
      • Analysis: how does each part of the sports car achieve this goal?
        • Example:  light-weight construction enables speed

1. Introduction

1.1. Background

Global temperatures and sea surface temperatures (SSTs) vary over ranges that include multidecadal to quasi-biennial. A current controversy concerns the presence and nature of decadal-scale slowdowns in global temperature anomalies, particularly the recent slowdown from about 1998 to the present [1,2]. This slowdown “has provided the scientific community with a valuable opportunity to advance understanding of internal variability and external forcing…” [3]. This paper will suggest a unifying and parsimonious physical (tidal) hypothesis to drive ocean/atmosphere variability and simulate the temporal variability of global temperature anomalies on timescales ranging from multidecadal to quasi-biennial. It is hoped that documenting the hypothesis would enable subsequent comparisons with other treatments.

Global temperature and its slowdowns have temporal patterns shared in other fields, for example the following: The Atmospheric Circulation Index (ACI) is a measure of winter wind-flow regimes from the Atlantic to West Siberia. Based on earlier work, Klyashtorin [4] classified the state of the ACI at a chosen time in terms of the accumulated difference between its zonal and meridional properties (herein referred to as Z-M). Using this formulation, the ACI exhibits a ~60-year oscillation, and regime change is signaled by a reversal in the accumulated ACI curve at a maximum or minimum. The temporal variation of detrended global temperature (and length of day, LOD) curves resemble the ACI Z-M parameter [4], although with differences of a few years in lead or lag times. The LOD varies over decades by milliseconds and is strongly correlated [5] with atmospheric angular momentum (AAM). In zonal wind regimes, the LOD increases when the earth’s rotation is slowed by a change in the earth’s mass distribution and an exchange of angular momentum between the earth’s surface and its atmosphere [6], a process promoted by precipitation or by evaporation over the oceans [7].

Dickey et al. [8] noted the common decadal variability of the LOD, and the angular momentum of the earth’s core and surface air temperatures, and found significant correlations with LOD leading model-corrected temperatures by eight years. They concluded that either oscillations in the core’s magnetic field modulated atmospheric factors, or that some other indirect effect of another fundamental process affected climate, or that there was another process that affects both.

In this journal, Oviatt et al. [9] reviewed some of these decadal patterns, drawing attention to zonal and meridional regimes that affect global temperatures, and described the effects on temperature of ocean upwelling. Global temperatures rise during zonal ACI regimes, and “pause” during meridional regimes. Following discussions at a recent workshop on decadal variability [10], the word “slowdown” will be used herein instead of the words “pause” or “hiatus” that have often been used to describe the arrested temperature rises in meridional regimes.

Oviatt et al. [9] listed three hypotheses to explain decadal shifts: (1) atmospheric–ocean interaction dynamics; (2) the rate of Atlantic meridional overturning circulation (AMOC); and (3) a statistical combination of climate indices and Arctic sea ice variability. They concluded there was no accepted causation to explain the decadal changes.

The first hypothesis includes the suggestion that the hiatus is associated with the negative phase of the Interdecadal Pacific Oscillation (IPO), and the accompanying cooling and strong easterly winds over the equatorial Pacific. The second hypothesis includes the idea that the warming hiatus is a result of large heat uptake by the deep ocean. From large ensemble simulations, Liu et al. [11] showed that, in hiatus decades, the Indian Ocean shows anomalous warming and accelerated ocean heat content increase below 50 m. This is associated with a La Niña-like climate shift and enhanced heat transport of the Indonesian Throughflow, and the warming occurs concurrently with Pacific cooling. Meridional overturning and wind-driven decadal variability in ocean basins were possible proximate causes. For further discussion of ocean heat uptake and global temperatures, see Whitmarsh et al. [12].

Several authors have noted the apparent relationship between the successive rises and pauses in global temperatures on the one hand and the temperatures and phases in Pacific-basin oscillations on the other (e.g., [1,2,13]). However, just ten of 262 model simulations with the Coupled Model Intercomparison Project Phase 5 (CMIP5) produced the early-2000s slowdown in global surface temperature rise from the decadal modulation associated with an IPO negative phase [14]).

Such empirical or computer-modeled relationships beg the question: What is the ultimate driver for ocean and climate variability? The seemingly close relationships between such oceanic, geophysical and climatic parameters may derive either from internally-generated and teleconnected terrestrial endogenous processes or through an external forcing mechanism. The possible sources of influences external to the climate system have generally focused on aerosols, volcanoes and solar irradiance, but such natural sources of variability seem to be inadequately represented in models; see for instance Trenberth [1] and Santer et al. [3].

This paper presents the hypothesis that exogenous tidal forcing from the sun and moon is a major cause of climate variability. The tidal hypothesis leads to the following propositions:
(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.

Relationships between tidal forces and climate variability may useful in long-term risk assessment for natural resource management, including fisheries applications described by Klyashtorin [4] and Oviatt et al. [9]. However, here, the hypothesis will be related only oscillations present in global mean surface temperatures and in some major climate systems on timescales from quasi-biennial to multidecadal.

1.2. The Tidal Hypothesis

The understanding of tidal effects from the sun and moon has progressed as a result of seminal studies [15,16,17], in the course of which the parameterization has become complex as more spectral components and terms have been added to the tidal potential; see for instance Kantha and Clayson [18].

Doodson [15] derived six fundamental astronomical frequencies governing the tides, with corresponding periods covering the range from a lunar day to almost 21,000 years. The three that seem most likely candidates to assist in explaining annual-to-multidecadal climate processes had periods of 18.847 and 18.613 years, corresponding to intervals involving the sun’s mean longitude, the longitude of the moon’s perigee and the longitude of the moon’s ascending node. Doodson expanded the number of tidal frequencies f by adding or subtracting these frequencies or their harmonics, such as with f1 + 2f2 − f3 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/distance3 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.

From time series analysis, high-frequency components in both directional senses were derived, showing that tidal maxima corresponded to events of close perigee coinciding with new moon. Some high-frequency components had nearly coincident maxima (“beats”) at decadal or multidecadal intervals. This beating method follows a procedure by Keeling and Whorf [20], which it must be said has been the subject of critiques by Munk et al. [23] and Ray [24], and has previously shown limited success in correlating with oscillations in the climate system. Tidal components derived from the present formulation show more success. The beating defined periods, phase angles (peak-and-valley timing) and amplitudes of multidecadal and decadal oscillations of “parent” and “daughter” tidal components (see for example [21], Figure 1), some of which seem not to have been previously identified or examined in relation to oscillations in atmospheric and oceanic components of the climate system. The defining feature of the approach is that the climate parameters discussed apparently respond to the coincidence of close perigee with new (or sometimes full) moon, which can be described generally as “close syzygy”.

The Appendix summarizes important features of the prior study [21] and the way they are extended to the present study. For example, it:
  • describes the zonal or meridional characteristics of the components;

  • explains the assumption that tidal periods are expected to be time-averaged;

  • describes small amendments to period and timing from the original data [21] based on tests for close syzygy with online Fourmilab software [25]; and

  • distinguishes between the treatment of the 18.60-year lunar nodal cycle in this and some previous studies of tidal forcing

It was suggested [21] that the 18.60-year oscillation could be represented as the 18.02-year saros cycle averaged over the 186.0-year “parent” cycle. The relationship is shown in the Appendix A to the present paper, and resembles a pattern (Keeling and Whorf, [20]) in which 18.02-year cycles fall within 186-year arcs. It should be noted that Ray [24] has expressed reservations about this and other features of the Keeling and Whorf paper.

1.3. Upwelling and Ocean Temperatures

Upwelling appears mainly off the west coasts of the continents (see [8]) or in the middle of the equatorial area of the oceans. Upwelling is induced by strong winds blowing over the ocean surface [26] and by tidal forcing of vertical mixing. Munk and Wunsch [27] concluded that the meridional overturning circulation may be mainly determined by the relatively small power of vertical mixing available to return the fluid to the surface layers. They considered four sources of the power needed to sustain abyssal mixing, and found that surface buoyancy forcing and geothermal heating were relatively unimportant, but that winds and tides accounted for most of the mixing: The sun and moon provide a total of 3.7 terawatts of tidal power, more than half the power needed for vertical mixing in the ocean. Keeling and Whorf [20,28] suggested that tidal periodicities produced climate effects through upwelling of cold water and consequent SST variability, and it is a focus of this paper to assess the degree of concordance between tidal periodicities and the temporal variability of ocean and global temperatures.

If tidal forcing drives zonal or meridional upwelling, then we expect that tidal forcing would be correlated with ocean temperatures. One might anticipate that the deduced pattern of tidal periods, phase angles and amplitudes would be most manifest in globally-averaged temperature data, but that individual ocean oscillations would experience different degrees of zonal or meridional forcing, and respond differently to the tidal components listed.

2. Materials and Methods

The only results carried forward from the Appendix A summary are the period and timing of the tidal components, the “beating amplitude” of the three multidecadal components (see below), and the assumption that tidal components and the climate oscillations responding to them vary in cosine form with the latter oscillation amplitudes being tidal-regime-dependent but constant during a regime. The number (seven) of periodicities generating tidal maxima at configurations of close perigee at new moon [21] is expanded in this paper. Although tidal component amplitudes are adjusted empirically to match the climate data, the periods and phases (timing of peaks and valleys) of the tidal components are essentially fixed by the prior analysis.

This paper denotes tidal frequencies by ν, and treats components derived by the close syzygy approach in a similar manner to the above: as fundamental frequencies, their harmonics and combinations. This approach leads to four fundamental frequencies which are apparently able, with their harmonics and frequency combinations, to simulate much of the quasi-biennial to multidecadal variability in temperature and ocean data. The four fundamental frequencies, denoted by ν1, ν2, ν3 and ν4, 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.

Testing the tidal hypothesis depends crucially on the timing of extrema (maxima and minima) in the cycles, which is in their various phase angles or, as characterized here, in their “reference times”. Working within this limit, tidal components derived from analysis generally have a significant statistical presence (p ≤ 0.05) in at least some of the oscillations to be described.

A causal relationship is possible if the period and phase (the timing of peaks and valleys) of a tidal oscillation coincides with the period and phase of an oscillation in temperature or another parameter. However, in cases with small differences in phase, one oscillation will lead and the other lag in time. If a temperature or other variable closely resembling a tidal analog, lags the analog by a small amount, then it is possible that the tidal oscillation causes the other oscillation. It is commonly found in research of this type that the lag time is small in relation to the period of the oscillation (such as a lag time of two months between two oscillations having a period of ten years). In such cases, the two oscillations are in virtual synchrony, allowing the possibility of a causal relationship between the two. This circumstance arises in this paper. A relatively small lag time may represent a reasonable interval for a stimulus to have its response. In an early part of this paper, a lag time of several years is proposed for a ~60-year oscillation, this lag reflecting the time taken for a proposed process of migration of released ocean gases to the upper atmosphere. The process will the explained below.

Climate-related oscillation data at decimal year time t can be compared with the tidal oscillations as captured by cosine relationships, in which the amplitude of a tidal oscillation at time t in decimal years is proportional to tlag0]/P) or tlag0]), where P is the component period in years, ν is the component frequency in reciprocal years, t0 (as described in the Appendix A) is the component reference time or “date-stamp” (1918.20 or 2039.96), and tlag 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: , where t represents the decimal year corresponding to an SST data point, and so on for other pairs of tidal and climate oscillations.

Groups of tidal components are introduced progressively in three sections covering multidecadal to quasi-biennial periods to simulate climate oscillations operating on corresponding timescales. These sections begin with components derived by the above beating process, and progress to harmonics and frequency combinations, all components related to close syzygy events. Prior to later discussion, a fourth section summarizes the relationships found between tidal components and the other climate oscillations considered.

The first three sections are discussed in the following terms:

(i) Multidecadal scale (Section 3.1):

The aim is to examine the degree to which a combination of multidecadal tidal components can simulate the ~60-year oscillation implicated as a cause of multidecadal fluctuations and slowdowns in global temperature [4]. The temperature data employed are HadCRUT4 (gridded monthly mean near-surface air temperatures from the Hadley Climate Research Unit, version 4) annual global mean surface temperature (GMST) anomalies, decadally smoothed with a 21-point binomial filter [29].

(ii) Intermediate-period scale (Section 3.2):

Following the multidecadal-scale simulation of smoothed anomaly data, this section examines the degree to which, after removing the ~60-year oscillation, tidal components having periods between the multidecadal set and a period of about 5 years can simulate the residual decadally smoothed GMST anomalies.

(iii) Short-period scale (Section 3.3):

This section examines the degree to which adding short-period tidal components can simulate unsmoothed climate datasets. The short-period tidal set is compared with: (a) HADCRUT4 unsmoothed annual GMST residual anomalies [29] from 1959 to 2016; (b) the University of Alabama in Huntsville (UAH) lower tropospheric (LT) temperatures generated from composite satellite data for the period 1979 to 2016 [30] and converted to annual data; and (c) the January to December annual increments in ppm carbon dioxide levels measured at Mauna Loa [31

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