Berry (Berri), B. L., D.Sc.

Cyclic Regularities in Global CLIMATIC, GLACIAL, PERIGLACIAL and geological HISTORY

Abstract

Oscillations with discrete periods (T_J=0.075 2^J/16y) under 2Ma have been patterned inside the Sun system. The laws of conservation of momenta create spectra: A_J = a_S T_J ², where A_J - amplitudes, a_S - constants for series of cycles. The cyclic regularities permit a common approach to the investigations of the terrestrial processes of the temperature distributions, sedimentation, geodynamics of landscape, tectonics and the creation of the time-space classification of landforms caused by tectonic and climate processes. Modern latitudinal permafrost has been created since 0.96 Ma BP. After the Arctic Ocean was covered by pack-ice (0.7 Ma BP) the long (~90 ka) glacial and short  (~10 ka) interglacial forced and auto-oscillatory processes have determined surface changes. Periodical fluxes of heat have destroyed the ice-sheets for only short times, but could not eliminate permafrost.

Introduction

Investigation into variations of climate, the temperature and composition of the lithosphere raise problems regarding the search for the source of cyclical processes. Climate variations during 3Ma B.P., revealed by the oxygen isotope ratio of a deep ocean sediment core, include the geological boundaries between the Pliocene and the Pleistocene Epoch (1,5Ma), between the Pleistocene and the Holocene Epoch, and the beginning of glacial and interglacial cycles, started around 0.7Ma B.P., when the positive feedback mechanism began operating to a stronger degree (Berry, 1998a,b).

1. The Discreteness of Galactic and Sun System’s Periodic Processes

The main sources of natural periodical changes are the processes of rotating and revolving of celestial bodies and their systems about their axes and centers of gravity. The current moment in time is tied to geological multi-million-year cycles, climatic thousand-year and intrasecular rhythms. The geological boundaries were created when the solar system rotated about the centre of Galaxy and entered periodically every 19 - 37 million years in jet streams of matter emerging from its gas-dust nuclear disc (Berry, 1993). The Sun system, as a resonance system, generates a discrete spectrum of natural oscillations, whose period (T_K) can be expressed by the equation (Berry, 1991):

                               T_K = T₀ 2^K/N     (1)

where T₀ = 27.32d = 0.075y - the Moon’s sidereal period, K - sequence of whole number, N = 16 - number of period into an octave (Oct.). A check of the physical-empirical formula (1) showed that the structure of rhythms with 16 periods into an octave has determined cosmic, solar and terrestrial processes, i.e., the Galaxy has a common system of discrete frequencies (Berry,1998b). The equation (1) is very convenient to classify cycles.

Natural periods of up to at least 2Ma have been formed inside the Sun system. Table 1 indicates the Pleistocene harmonics based on oxygen-isotope (Hays et al., 1976, Raymo, 1992, Berry, 1993) and on astronomical data (Brouwer, Woerkom, 1950, Monin, 1982, Zubakov, 1990). These cycles of the Sun system have been fixed in sedimentary rocks of different geological periods in the glacial and mild climatic epoch, but not only in stratums of the Pliocene and the Pleistocene Epochs.

Table 1. Terrestrial (T_T ), Astronomical (T_A ) and Theoretical (T_K) Periods of the Range 10 - 1000 Thousand Years.

2. Amplitude-Period Relations

Planets create 99.5% of the moment of revolving momentum of the solar system, although their total mass is around 0.1% of the Sun’s mass. Celestial bodies have the same perturbate periods, but of course these periods have different amplitudes, because all planets and the Sun have various radii and masses. The relationship between periods (T_j ) and radii (r_j ) can be derived from the law of conservation of moments of revolving momentum (M_{j rev} ):

                                                  r_j m_j v_j  = M_{j rev} ;      2p m_j r_j² / T_j = M_{j rev} ,    or        r_j = (M_{j rev} / 2p m_j )^1/2(T_j )^1/2   (2)

where T_j  and v_j - the orbital period and velocity.

The law of conservation of moments of angular momentum (Mjang) creates a similar picture for the rotations of planets and the Sun around their central axes. The form of celestial bodies, including the solar and terrestrial ellipsoids, has been transformed by the gravity of other planets and that automatically changes the period (T_j) or the frequency (F_j) of rotation, the radii (R_j) of ellipsoids, or amplitudes (A_j ) of variations:

(2/5) 2m_j R_j2 F_j = Mj ang or  R_j = (5M_{j ang} / 2p2 m_j )^1/2(T_j)^1/2                 (3)

Comparison of equations (2 and 3) has shown that we have had specific oscillations, which display the following relationship between Aj and Tj (Berry, 1991):

Aj2Fj = cj ,               Aj = (cj Tj)1/2,          or            Aj = s (Tj )1/2,            (4)

where s = (cj )1/2, c_ang=5M_{j ang}  /2p2 m _j , c _rev =M _{j rev} / 2p m _j .

Periods  Tj  and amplitudes Aj are variable, but s  is constant for homogeneous series of natural cycles. These spectra relate to basic physical laws and are detected in all processes. It is important that the coefficient s be used to classify them.

2.1. The Area - Thickness Relationship of Landforms

2.1.1. Planetary Forms

We begin this analysis with the space waves of planetary relief (R ). The average longitude (dimension) of continent, ocean, and other terrestrial objects (D_RJ) is an analog of the period of the wave, and the maximum height or depth (H_RMJ) is an analog of the amplitude., i.e.:

H_RMJ = a_RM ( D_RJ ) ^1/2 ,   (5)

where   a_RM km^1/2 - is the coefficient for the planetary relief, D_RJ = S_RJ^1/2, S_RJ - the area of an object. When   

  a_RM= 0.0906 km^1/2,  (6)

the standard error of determination H_RMJ equals about 10% for all oceans and continents. Europe and Asia, Australia and Oceania were considered as two united continents.

2.1.2. Glaciers

A similar relationships can be found for glaciers of different types. For example, in accordance with equation (5), the volume of the glacier with isometric area can be written in the form:

V_GJ = H_GAJ S_GJ =   a_GA(D_GJ )^1/2 (D_GJ )² =   a_GA(D_GJ )^2.5 =   a_GA(D_GJ²) ^1.25 = a_GA(S_GJ ) ^1.25  (7)

where H_GAJ = _GA(D _GJ)^1/2 is the average thickness of the glacier, S_GJ and V_GJ are the area and volume of the glacier,

for average thickness H_GAJ       a_GA = 0.309 km^1/2,    (8)

and for maximum thickness H_GMJ      a_GM = 0.671 km^1/2. (9)

The giant glaciers of Greenland and the Antarctica are included in the series.

2.1.3. Permafrost

If we accept the distributions of latitudinal permafrost (P) in Asia (A) presented by I. Ya. Baranov and Shi (French, 1996):

S_PA = 119 (Russia) + 0.8 (Mongolia) + 0.4 (China) = 12.2 Mkm²,

 and in North America (NA) by Washburn and Rott (French, 1996):

S_PNA = 4.69 (Canada) + 1.25 (Alaska) = 5.94 Mkm²,

and the maximum depths - 1600 and 1000m accordingly

we can estimate  a_PA = 0.027  and   a_PNA = 0.020 m^1/2       

and the average value  a_PM = 0.0235 m^1/2.  (10)

For the average value  a_PM  the maximum thicknesses of permafrost in North America and Asia have the following magnitudes in accordance with the equation (5): H_PMNA=1.16km, H_PMA=1.39km. These figures coincide well with the real data. The climatic conditions and the geothermal gradients are related to the areas of continents and permafrost, so we can use one coefficient  a_PM  for this case.

2.2. The Time - Thickness Relationship of Landforms