This paper analyzes relationships between the quasi-biennial oscillation of stratospheric winds (QBO) and El Niño with the Southern Oscillation (ENSO). Dr. Karlstrom looks at the available data as well as data he has collected to determine a correlation (whether linear or nonlinear) if one exists between these two. The general circulation models (GCMs) are designed for predicting weather events, and Dr. Karlstrom’s goal is to test these models and see what may be missing from them. The more accurate information and parameters used in the GCMs, the better prediction one gets.

Dr. Karlstrom uses various records to test the Milankovitch/Pettersson Climatic Theory, also referred to as the Solar-Insolation/Tidal Resonance Climate Model. Using data records of high-frequency weather events, Dr. Karlstrom can compare the correlation effect to the general circulation models’ results and determine if these events do in fact line up with the Tidal Resonance Model. If these weather events—specifically the QBO and ENSO in this paper—line up with the model, it would be a serious asset to the concept of natural climate change. Knowing this, Dr. Karlstrom looked at a variety of cycle records to compare atmospheric variations with the tidal resonance models. 

The figures used in this paper are climatic records plotted with tidal resonance cycles to determine if the data matches the model. The general timescale for these figures and records is based on the 556-year Phase Cycle, which ranges from 1433-1989. Some of the figures have the correlation coefficient calculated, written R. This number ranges from -1 to 1 and is a percentage of the amount of data that matches between cycle turning points and paleoclimatic trend. A percentage close to 1 suggests an almost linear relationship between the data, so the closer to 1 R is, the more the data agrees with each other.

Figure 1’s data is taken from Alaskan bioclimatic and chronostratigraphic data, which agree well with the Phase Cycle presented since the correlation coefficient is close to 1. Figure 2 plots high-resolution records taken from European bogs. This figure suggests that the post-glacial warm/dry period recorded in central and northern Europe line up with North America’s from 6000 to 5000 years before present. The data in Figure 3 is used to derive the European Alps’ Postglacial timberline record. Figure 4 depicts the dendroclimatic cycle with the tidal resonance cycle. The precipitation and temperature records used come from White Mountain and the Sierra Nevada, California; Colorado Plateaus; Hopi Mesa; and Tsegi Canyon. These records have an R-value of 0.86, meaning there is an 86% of match between cycle turning points and the paleoclimate trend. Figure 5 compares climate and sunspot records (taken from Santa Barbara and Iceland) with the Tidal Resonance Model with the result of an apparent positive correlation between them.

Sunspots, tree-ring records, and solar tides are taken from the Midwest and Colorado Plateaus fuel Figure 6. This data seems to match up with the Hale double sunspot cycle, which then relates a positive solar magnetism with a general increase in rainfall on earth. Figure 7 begins to analyze the QBO with the (556-year) tidal resonance model, resulting in a correlation coefficient of 0.93. There is a strong relationship between the QBO record and a portion of the Tidal Resonance Model (specifically, the 2.32-year resonance). Figures 8 and 9 are extensions of the data in Figure 7, comparing the QBO with average global temperature records and sunspot data to the model.

The final figure, Figure 10, relates many records to the Event Cycle (1850-1989). These records include the QBO, El Niño, and tropical air pressure and temperature. This final figure plots all of these records with the portion of the 556-year Phase Cycle that produced a strong correlation with the QBO. When comparing this same cycle with tropical air pressure and temperature records, the result was a correlation coefficient of 0.82. However, the El Niño- Southern Oscillation correlation coefficient (of 0.51) is tremendously weaker, which suggests that GCMs are missing critical parameters that would affect the predictions of El Niño events. Dr. Karlstrom’s research has shown how various climatic and atmospheric records do line up with the Tidal Resonance model, thus suggesting that there is a climate cycle rather than it being random events.

The QBO, El Niño, and Tidal Resonance Model

by Thor Karlstrom

The QBO and ENSO

            The QBO winds in the lower stratosphere alternate from easterly to westerly regimes, with a mean period estimated by various researchers at about 26, 27, or 28 months (2.2-2.3 years). The winds originate earliest at the higher altitudes, have maximum velocity at an intermediate level, and dissipate gradually downward at a uniform rate of about 1 kilometer/month to disappear near the tropopause. Because these wave trains are initiated at higher altitudes and transgress time in downward propagation, one might suspect a forcing function at the top. However, similar stratospheric oscillations have been simulated in GCMs (general circulation models) based on the dynamic interplay of tropical tropospheric and oceanic parameters plus the ad hoc inclusion of the effects of equatorial eastward-moving Kelvin Waves and the slower westward-moving Rossby Waves, which evidently set up a delayed response oscillation (Takahashi and Boville 1992 in Coriolle et al 1993). GCMs expanded to include the effects of adiabatic processes (radiation, convection, precipitation, and latent heat) also simulate QBO-type waves in the stratosphere but without any ad hoc parameterization of equatorial wave forcing (Coriolle et al 1993). This suggests that such oscillations are inherent in the lower atmosphere/ocean system and are transmitted upward into the stratosphere by wave-breaking (momentum deposition). The amplitude of these simulated oscillations, however, is significantly less than the observed value, suggesting that an additional amplifying source may be missing in the model.

            The GCMs designed to predict the recurrence of anomalously warm surface water, higher sea level, and downwelling in winter along the west coast of South America (El Niño) principally include the major oscillating pressure system of the tropics (the Southern Oscillation) and the interacting Kelvin/Rossby wave model. The Southern Oscillation largely determines temperature, precipitation, and wind changes in the tropics; the wave model facilitates the recurring eastward movement of warm surface water formed principally in the western Pacific. Correlation of El Nino with the Southern Oscillation has resulted in designation of the combined systems as ENSO. Failure of most ENSO models to predict some El Niños (Kerr 1993) has led to the suggestion that the erratic timing of El Nino is a function of a low-order transition to chaos through a series of frequency-locked steps created by nonlinear resonance forced by the annual cycle (Jin et al 1994; Tziperman et al 1994) and, thus, by implication unpredictable—on the way to chaos, but not quite.

Resonance Analysis

            Since this analysis focuses on higher frequency components of the weather, I begin by placing them in context with lower-frequency elements of the tidal-resonance climatic model. Figures 1 through 6 are examples of paleoclimatic records suggesting in-phase relationships with the 556-year tidal cycle and its 2/1 (278-year), 4/1 (139-year), 6/1 (92.7-year), 12/1 (46.3-year), and 25/1 (22.2-year) resonances.¹ Figures 1, 4, 5, and 6 are slight modifications of figures presented in Karlstrom (1995); Figures 2 and 3 have not been previously published. The coefficient of correlation (R) shown in these and subsequent figures represents the percentage of match by inspection between paleoclimatic trend and cycle turning points.

¹ The ratio indicates frequency change relative to the base cycle as 1; the resulting subharmonic resonance is identified by wavelength in the accompanying parentheses.

            The above resonance correlations suggest doubling, tripling, and redoubling of a forcing cycle, a phenomenon characteristic of a complex dynamic system in nonlinear transition to chaos, although linearity cannot be excluded at the present level of analysis.

Figure 1-Bioclimatic record of Home Bog, Cook Inlet, Alaska, on time-scale of the 1112-year Stadial Cycle and its 2/1 (556-year) Phase Cycle and 4/1 (278-year) Subphase Resonance. Pollen indices in Heusser (1965) time-calibrated by basal date listed in Karlstrom (1964). The higher frequency Girdwood Bog record is schematically plotted as interpreted climatically in Karlstrom (1961). Because of wider sampling intervals, Homer Bog shows the strongest tendency to oscillate in phase with the 556-year Phase Cycle and positions the driest post-glacial interval contemporaneous with the late Atlantic dry interval of Europe (see Figure 2). (AC = Altithermal Culmination)

In Figure 1, Alaskan bioclimatic and chronostratigraphic evidence suggests the 556-year Phase Cycle and its double 2/1 (278-year) resonance.

           

In Figure 2, these resonances appear to be recorded in examples of European bog records with primary trends suggesting that the major post-glacial warm/dry interval of northern and central Europe were contemporaneous with that in North America, culmination between 6000 and 5000 YBP.

Figure 2-Cook Inlet paleoclimate and collated European high-resolution records on timescale of the 1112-year Stadial Cycle and its 2/1 (556-year) and 4/1 (278-year) resonances. A. Cook Inlet, Homer Bog (Figure 1); B. Agaröds Bog/hydrology of Sweden (Nilsson 1964); C. Alps timberline fluctuations (Beug 1982); D. Danish Bolling Bog (in Karlstrom 1961); and E. Swiss Wachseldorn Bog (Oeschger and others 1980) which, though more complacent (lower amplification of secondary oscillations), replicated with some fidelity the classic Late Glacial Dryas sequence of Denmark in D. Data used in constructing Alps record C are shown in Figure 3. (AC= Altithermal Culmination)

Figure 3 provides the data used in constructing the Postglacial timberline record of the European Alps.

In Figure 4, southwest dendroclimatic records suggest a regionally robust Event Cycle of 139-years, which represents doubling (2/1) of the 278-year Subphase Cycle and a redoubling (4/1) of the 556-year Phase Cycle.

In Figure 5, paleoclimatic records suggesting the 6/1 (92.7-year) and 12/1 (46.3-year) resonances seem to be directly related to solar activity as expressed in Sunspot Cycle length and could be either linear or nonlinear in origin.

Figure 3-Paleoclimate of the European Alps inferred from pollen-derived timberline shifts. From Paleoecological data summarized in Beug (1982). Main trends from averaged elevations of five curves reconstructed, respectively, for the Alps of Austria, France. Wallis, northern and south-central Switzerland. The superimposed named secondary cold phases (number of events shown in parentheses) are from various workers in different parts of the Alps. The plotted amplitudes of these radiocarbon-bracketed cold phases are relative and not to scale. “Modern” events after Patzelt (1980). Time-scale in years before present (1950). >-< = Bracketing radiocarbon dates.

Figure 4-Summary evidence for a dendroclimatic cycle in phase with a 139-year tidal force resonance. Trend correlations, both in temperature and precipitation, range from 0.75 to >0.9, or within the range of correlations from tree-ring/climate calibrations. This suggests that the cycle is real, regionally robust, and related to changing atmospheric dynamics and patterns. Similar half-cycle analyses of other records may define differing regional patterns and local responses, advancing understanding of climatic/biologic process. PB = point boundary (clustering of basal contact dates; Karlstrom 1988). 1: White Mountain, California, 10-year precipitation indices (Fritts 1967). 2: Sierra Nevada, California, 10-year temperature indices (Scuderi 1987). 3: 1 and 2 combined (precipitation and temperature). 4: White Mountain, California, 20-year precipitation and temperature indices (Lamarche 1974). 5: Sierra Nevada, California, 20-year temperature indices (Graumlisch 1992). 6: Colorado Plateaus 17-station 10-year precipitation indices (Berry 1982). 7, 8, 9: Annual precipitation indices from Dean and Robinson (1978).

Figure 5-Sunspot and climate records on timescale of the 139-year Event Cycle and its 3/1 (46.3-year) and 12/1 (11.5-year) resonances.

Sunspot, hemispheric temperature, and Iceland indices to 1745 from Friis-Christensen and Lassen (1991); extension of Iceland temperature record by indices from Bergthorsen (1969). Santa Barbara marine indices from Pandolfi and others (1980), and tree-ring-dated isotope indices from Epstein and Tapp (1976). Sunspots and collated climatic records appear to be related to the Tidal Resonance Model through in-phase relationships with the ~46-year resonance and its 2x Gleissberg Sunspot Cycle. Some tendency for sunspot-length and higher resolution climate records to oscillate in phase with the 11.5-year resonance.

In Figure 6, the 25/1 (22.2-year) resonance also appears to be directly related to solar activity but, in the case, with solar magnetism (the double Hale Sunspot Cycle). Thus, resonance could also be a function of either linear response or a fundamental fifth produced in a nonlinear transitional phase toward chaos. These apparent frequency-dependent correlations with both Sunspot length and Solar magnetism emphasize the potential complexity (and remaining uncertainty) of the mix of processes seemingly involved in tidal/solar influence on weather.

Figure 6-Solar tides, sunspots, and dendroclimatic records on timescale of the 2/1 (278-year), 4/1 (139-year), and 25/1 (22.24-year) resonances of the 556-year phase cycle. Annual indices of sunspots and solar tides from Wood in Gribbin (1976); of midwest tree-ring indices from Mitchell and others (1979) in Burroughs (1992); and of Colorado Plateaus tree-ring indices from Dean and Robinson (1978). Half-cycle smoothing on turning points of the 25/1 (22.24-year) resonance that is in phase with the average Hale double sunspot (magnetic) cycle. This, in turn, seemingly integrates solar/earth tidal phases with terrestrial climate through solar magnetic change (+ solar magnetism = generally increased earth rainfall).

In Figure 7, I extend analysis to higher frequencies by comparing two resonances of the tidal-force model that approximately match the mean period of the QBO as represented by indices derived from Figure 5.8 in Burroughs (1992). The 250/1 (2.22-year) resonance of the 556-year tidal cycle tests the repeated suggestion in the literature that the QBO may be the fifth resonance of the mean Sunspot Cycle (11.1-years). The slightly longer 240/1 (2.32-year) resonance is intrinsically much stronger in that it is a combination of resonance components divisible by all integers through 10, expecting the weak 7^th and 9^th. Figure 7 shows that the 250/1 resonance is evidently too short for consistent in-phase relationships with the QBO, whereas the 240/1 resonance appears to be strongly in phase with the QBO both in timing (as extrapolated over 500 years from AD 1433) and in average duration. Burroughs (1992) gives the mean period of the QBO as about 28 months. The 2.32 years (27.8 months) of the 240/1 resonance is essentially the same. Nonetheless, a much longer QBO record is required to more precisely define mean cycle length and to statistically exclude the possibility of fortuitous coincidence within the present short segment of record.

Figure 7-The quasi-biennial oscillation of stratospheric winds (QBO) on timescale of the 556-year Phase Cycle and its 240/1 (2.32-year) and 250/1 (2.22-year) resonances. The two resonances produce a beat cycle every 55.6 years when they return to phase, or ten times during each Phase Cycle. The 240/1 resonances appears strongly in phase with the QBO record; the 250/1 resonance (one-fifth of the average Sunspot Cycle) is evidently too short for consistent in-phase relationships with the QBO. Monthly indices from Figure 5.8 in Burroughs (1992) replotted at 3-month intervals.

In Figures 8 and 9, I extend analyses of these two resonances through correlation with Jones and Wigley’s (1990) version of average global temperature. Whereas the 240/1 (QBO?) resonance may be weakly represented (Figure 8), no correlation in phasing is apparent with the 250/1 (Sunspot) resonance (Figure 9). However, as graphed in Figure 9, the progressive decrease in Sunspot length toward the end of Phase Cycle Z is consistent with Friis-Christensen and Lassen’s (1991) longer term correlation of decreasing Sunspot length with increasing global temperature–and evidently with the tidal resonance model as well (Figure 5).

Figure 8-Correlation of QBO and average global temperature record on timescale of the 556-year Phase Cycle and its 48/1 (11.58-year) and 240/1 (2.32-year) resonances. Annual average temperature indices from Jones and Wigley (1990); monthly QBO indices from Burroughs (1992) replotted at 3-month intervals. Although the QBO easterlies seem strongly in phase with the 240/1 resonance, it is apparently only weakly reflected in the secondary trends of Jones and Wigley’s version of the global temperature record. Compare with Figure 9.

Figure 9-Correlation of QBO and average global temperature record on timescale of the 556-year Phase Cycle and its 50/1 (11.12-year:Sunspot Cycle) and 250/1 (2.22-year) resonances. Annual temperature indices from Jones and Wigley (1990); monthly QBO indices from Burroughs (1992). The 5/1 resonance of the average Sunspot Cycle (though showing a tantalizing strong tendency for association with the westerly wind epicycle) is evidently too short for consistent phasing with the QBO and apparently is not reflected in Jones and Wigley’s version of global temperature. Sunspot schemata from Figure 6. Solid lines = observed turning points of the numbered Sunspot Cycles. Note the progressive decrease in cycle-length toward end of Phase Cycle Z, or consistent with Friis-Christensen and Lassen’s (1991) correlation of shortening cycle-length with increasing global temperature (Figure 5).

In Figure 10, a much stronger correlation is suggested between the 240/1 (QBO) resonance and the Southern Oscillation tropical air-pressure/temperature records. The result is generally compatible with the GCMs that generate QBO-type stratospheric winds from tropospheric circulation dynamics and with energy transfer from troposphere to stratosphere. The seemingly stronger correlation of the 240/1 resonance with the QBO than with the Southern Oscillation, however, suggests that tidal-resonance modulation or amplification in the stratosphere is more linear that that in the denser lower atmosphere. If, in fact, the out-of-phase portions of both records represent nonlinear phase reversals, the larger number of such reversals in the ENSO suggest sporadic decoupling of the two systems, both of which evidently occasionally respond differentially to the same driving function.

The correlation with the El Niño series is strikingly weaker, suggesting that some critical parameter(s) has been missed in modeling the ENSO. Most El Niños coincide with Southern Oscillation temperature troughs but are missing or displaced during others. Independent analyses by Jin et al (1994) and Tziperman and other (1994) are consistent in suggesting that the seasonal El Niño phenomenon is a function of a low-order nonlinear transition to chaos forced by the annual cycle. After all, they none, El Niño is a winter phenomenon. But some El Niños still phase with the resonance model. Missing 1989 (no El Niño, presumably because of nonlinear phase reversals in both QBO and ENSO records), the model predicted the 1991 and 1993 El Niños and predicts El Niños for 1996 and 1998 if no nonlinearities or other distorting variables intervene. A big if, implying that unless missing variables are found, or unless timing and phasing of nonlinearities become predictable by refined theory or precursor signals, El Niño and other higher frequency weather phenomena will remain essentially unpredictable over the long run.

Figure 10-The QBO, tropical air pressure/temperature, and El Niño records on timescale of the 240/1 (2.32-year) resonance of the 556-year Phase Cycle. Tropical temperature indices from Burroughs (1992), ENSO indices from Kerr (1993), Jakarta air-pressure indices from deBoer (1967), and El Niño dates from Quinn and others (1987). The generally strong correlation of the QBO and SO/temperature with the 240/1 resonance strongly suggests tidal-force modulation of one or both of these stratospheric and tropospheric oscillatory systems. The El Niño-Southern Oscillation correlation is strikingly weaker, suggesting that other critical variables are involved, including possible nonlinear phase-reversals near 1961 and 1989 in the QBO, and near 1958, 1968, 1982, and 1989 in the air pressure/temperature records. Alternatively, these differences could result from nonlinear response to the annual cycle.

Summary

The recent application of Chaos Theory to atmospheric dynamics seems to provide an explanation for some of the perplexing order/disorder patterns of high-frequency weather records. However, even the longest, instrumental records (about 100 years) are too short to permit statistical discrimination between random events and nonlinear responses (Tziperman et al 1994) or, for that matter, between linear and nonlinear responses. With this caveat, I tentatively conclude the following:

The fifth resonance (2.22 years) of the Sunspot Cycle (= the 250/1 resonance of the 556-year tidal-force cycle) is seemingly too short to match the oscillations of the QBO which, therefore, is probably not directly driven by solar processes.

 

Instead, a strong match, both in timing and average duration, with the intrinsically stronger 240/1 (2.32-year) resonance of the 556-year tidal-force cycle, strongly suggests that the QBO may be either modulated or amplified by atmospheric tidal resonances.

The generally strong correlation between the QBO and tropical Southern Oscillation, in turn, suggests that one or probably both of these stratospheric and tropospheric oscillations are modulated or amplified by the same tidal-resonance system. The greater number of presumed nonlinear phase reversals in the ENSO record, however, suggests that the two atmospheric levels are coupled loosely enough to permit occasional differential nonlinear responses to the same driving function. Parameterization of modulating tidal resonances may improve some GCMs by increasing the amplitude of the simulated QBO-type oscillations.

The strikingly weaker correlation between the Southern Oscillation and El Niño events strongly suggests that some critical parameters are missing in the GCMs specifically designed to predict El Niño occurrence. The missing ingredient may be low-order nonlinear phases during transition to chaos as driven by the annual cycle. Another possible explanation for El Niño irregularity as occasional nonlinear phase reversals. In any case, unless missing variables are found, or unless nonlinearities become predictable by refined theory or precursor signals, the timing of El Niño will probably remain unpredictable. Thus, in high-frequency weather analyses, we may be on a journey toward chaos but still not quite there.

Acknowledgements

            To my wife, colleagues, and friends who have urged me to continue my decades-long research on high-resolution paleoclimatic records.

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