A.Mary Selvam

Indian Institute of Tropical Meteorology, Pune 411 008, India

(Retired) email: selvam@ip.eth.net

web site: http://www.geocities.com/CapeCanaveral/Lab/5833

*Proc. International Geoscience and Remote
Sensing Symposium (IGARSS'87), 18-21 May 1987, Michigan, USA.*

Abstract

Observations show that
geomagnetic field lines follow closely the atmospheric circulation patterns
(Gribbins, *New Scientist*, **5 Feb**., 350-353, 1981). and that
geomagnetic field variations are precursors to climate change ( Courtillot
*et
al*., *Nature* **297**, 386-387, 1982). Therefore close monitoring
of the local and global geomagnetic field variations by satellite systems
will assist prediction of hurricane tracks, intensification and also long-term
weather trends. The exact mechanism for the observed close relationship
between global geomagnetic field and the tropospheric weather patterns
is not clear. In this paper a universal theory of atmospheric eddy dynamics
is presented which shows that the global geomagnetic field, atmospheric
electric field and weather systems are manifestations of a semi permanent
scale invariant hierarchical atmospheric eddy continuum. The scale invariant
energy structure for the atmospheric eddy continuum has been documented
and discussed ( Lovejoy and Schertzer, *Bull. Amer. Meteorol. Soc*.,
**67**,
21-32, 1986). In summary, quantitative equations are derived to show that
the full continuum of atmospheric eddies exist as a unified whole and originate
from buoyant energy supply from frictional turbulence at the planetary
surface ( Mary Selvam *et al*., *Proc. VII Int'l. Conf. Atmos. Elec*.,
June 3-8, 1984, Albany, N.Y., 154-159). Large eddy growth occurs from turbulence
scale by the universal period doubling route to chaos ( Fairbairn, *Phys.
Bull*. **37**, 300-302, 1986). The turbulent eddies are carried upwards
on the large eddy envelopes and vertical mixing occurs by the turbulent
eddy fluctuations resulting in downward transport of negative space charges
from from higher levels and simultaneous upward transport of positive space
charges from surface levels. The eddy circulations therefore generate a
large scale vertical aerosol current which is of the correct sign and magnitude
to generate the horizontal component of the geomagnetic field. Therefore,
atmospheric circulation patterns leave signature on the geomagnetic field
lines whose global variations can be easily monitored by satellite borne
sensors and thus assist in weather and climate prediction.

**Introduction**

Numerous studies indicate
correlation between geomagnetic field variations and tropospheric weather
activity ( Herman and Goldberg, 1978; Gribbins, 1981; Courtillot *et
al*., 1982; Kalinin and Rozanova, 1984; Taylor, 1986 ). However, the
exact physical mechanism for the observed coupling between meteorological
and geomagnetic phenomena is not yet identified. In this paper a gravity
wave feedback mechanism for the troposphere-ionosphere coupling is proposed.

**Physical Mechanism**

Vertical mass exchange
in
the troposphere-ionosphere-magnetosphere takes place by means of an eddy
continuum. Any perturbation in the troposphere would be transmitted to
ionosphere and vice versa. A global perturbation in the ionosphere, as
the one caused by solar variability, is transmitted to troposphere influencing
weather systems/geomagnetic/atmospheric electrification processes ( Mary
Selvam *et al*., 1984; Poonam Sikka *et al*., 1984 ).

The atmospheric boundary
layer ( *ABL* ) contains large eddies or helical vortex roll
circulations as seen from well organized cloud rows, cloud streets and
meso-scale cloud clusters ( *MCC *) in global satellite cloud cover
pictures ( Eymard, 1985 ) . It is however not clear how such long-lived
circulations exist in the dissipative turbulent planetary boundary layer
flows. In the following it is shown that the buoyant production of energy
by micro scale fractional condensation ( *MFC *) in turbulent
eddies is responsible for the sustenance and growth of large eddies in
the atmospheric boundary layer ( *ABL *) (Mary Selvam and Murty, 1985;
Mary Selvam, 1986; Mary Selvam and Murty, 1987; Mary Selvam, 1987). The
circulation speed of the large eddy is related to that of the turbulent
eddy according to the following relation ( Townsend, 1956) .

(1)

where

Figure 1 : Conceptual model of large and
turbulent eddies in the *ABL*

The turbulent
eddy fluctuations mix overlying environmental air into the growing large
eddy volume and the fractional volume dilution rate ** k** of
the total large eddy volume across unit cross section on its envelope is
equal to

(2)

where (3)

(4)

The rising large eddy gets
progressively diluted by vertical mixing due to the turbulent eddy fluctuations
and a fraction From Eqs. (2) and (3)

(5)

Therefore
The steady state fractional upward mass
flux of surface air is dependent only on the dominant turbulent eddy radius.

**Eddy Energy Spectral Slope**

The eddy energy power
spectrum is conventionally plotted as ** ln E** versus

The spectral slope ** S** of the
scale invariant eddy energy continuum is given as

*S = ln E / ln z***
= -2 ** for large

(6)

Therefore the universal period doubling route
to chaos eddy growth mechanism gives rise to an eddy energy continuum spectral
slope equal to **Quantum Mechanical Nature of the Eddy
Energy Structure**

The kinetic energy ** KE**
per unit mass of an eddy of frequency

eddy in the continuum is equal to the integrated mean of all the inherent turbulent eddy circulations. Let

Therefore *2 R =
W _{p} / *

** H** is equal to the product
of the momentum of unit mass of planetary scale eddy and its radius and
therefore represents the spin angular momentum of unit mass of planetary
scale eddy about the eddy center. Therefore the kinetic energy of unit
mass of any component eddy of frequency

**Normal Distribution Characteristics
of the Eddy Energy Perturbation Field**

Natural phenomena posses
energy/geometrical structure which is found to follow statistical normal
distribution characteristics. Such normal distributions conventionally
attributed to random chance, are in reality the deterministic laws of the
unified eddy dynamical processes, and therefore represent the implicit
order in natural phenomena as shown in the following. Let ** P**
represent the probability of occurrence in the medium of bi-directional
energy flux with characteristics of a particular large eddy radius

** W/w_{*}**
is distributed normally since

The period doubling sequence for eddy growth gives

*r = (dR/R) = 1/2*

The standard deviation ** s
**with
a cumulative probability of occurrence equal to

**Physical Meaning of Normal Distribution
Parameters**

The statistical distribution
characteristics of natural phenomena commonly follow normal distribution
associated conventionally with random chance. The normal distribution is
characterized by the *moment coefficient of skewness* equal to ** zero**,
signifying

From Eq.3

** (dW)^{4} / w_{*}^{4}**
represents the statistical

** (dz/z) = 2** for one length
step growth by period doubling process since

Therefore *moment
coefficient of kurtosis* is given as

In other words, period doubling phenomena
result in a threefold increase in the spin angular momentum of the large
eddy for each period doubling sequence. This result is consistent since
period doubling at constant pump frequency involves eddy length step growth
** dR**
on either side of the turbulent eddy length

**Physical Meaning of the Universal Feigenbaum's
Constants of the Period Doubling Route to Chaos**

The universal period
doubling route to chaos has been studied extensively by mathematicians.
The basic example with the potential to display the main features of the
erratic behaviour is the *Julia* model ( Delbourgo, 1986 ) given below.

*X _{n+1} = F( X_{n}
) = L X_{n} (1 - X_{n} )*

The above non-linear model represents the
population values of the parameter ** X_{n} **at
different time periods of

The universal constants

The physical concept of large eddy growth by the period doubling process enables to derive the universal constants

From Eq.(1) the function

(8)

** a** is therefore equal
to

Let

(9)

Therefore ** 2a^{2}
= 3d** from Eqs.(8) and (9). The variable

**Model for Atmospheric Electric and Geomagnetic
Field**

In the following it
is shown that the atmospheric electric field and geomagnetic field variations
are manifestations of the vertical mass exchange process between the lower
troposphere and ionosphere. The vertical mass exchange on the sunlit hemisphere
gives rise to upward transport of surface air. The nuclei in the surface
air layers contain a net positive space charge and thus there is an aerosol
current *i _{a*} = w_{*} *

*s =s _{*}
f*

(10)

The atmospheric electric field *F = 4 ps*

(11)

The computed vertical profile of electric
field

Figure 2 : The computed vertical profile
of ** F** and

Figure 3 : The observed vertical profile
of condensation nuclei ** s**andelectric
field

The aerosol current at any level ** z**
is given as

*i _{a} = (s_{*}
f z) x ( w_{*} f z ) = i_{a*} f ^{2 }
z^{2}*

(12)

Thus the aerosol current ** i_{a}**
produced by the vertical mass exchange generates the observed atmospheric
electric field. The conventional air earth conduction current ( Chalmers,
1967 ) cannot discharge the atmospheric electric field thus produced since
the dynamic charge transport by the vertical mass exchange process is faster
than the ion mobilities by more than one order of magnitude. The convective
scale aerosol current can be computed from Eq.(12) and shown to be

Observational evidence for the tropospheric eddy continuum extension into the ionosphere is seen in satellite observations which indicate that increased currents at ionospheric levels are accompanied by a simultaneous increase in wind speed at lower levels. Measurements with

The solar wind energy coupling in the terrestrial magnetosphere is indicated by the geomagnetic micropulsations and therefore also signal the continuous solar wind energy supply modulation of

**Planetary Atmospheric Energy Exchange
with Extra Terrestrial Environment**

The scale invariant
self-similar atmospheric eddy continuum generated by the universal period
doubling route to chaos growth process exists as a unified whole , spanning
the total planetary atmospheric boundary layer from the planetary surface
to the outermost limits of the magnetosphere and is in constant two-way
communication for energy flow from solar and other planetary/stellar atmospheres.
The fine structure signal of the unified atmospheric eddy continuum is
manifested as the luminescence phenomena of the auroral oval, where field-aligned
currents in discrete auroral arcs indicated bi-directional eddy enegy/charge
flow. Field aligned currents in discrete auroral arcs are visible manifestations
of atmospheric vertical mixing coupled to solar wind pumping of negative
space charges downwards accompanied by simultaneous upward transport of
terrestrial positive ions. Therefore, the aerosol currents originating
from the planetary surface extend into the magnetosphere in the discrete
auroral arcs and couple to the solar wind energy pump accounting for the
observed close association between solar wind dynamic parameters , discrete
auroras and geomagnetic micropulsations ( Feldstein and Galperin, 1985
) . Therefore ground based monitoring of geomagnetic micropulsations will
indicate the extra-terrestrial energy flow rate into the planetary atmosphere.
The above theory proposed for *magnetosphere - ionosphere - troposphere*
energy coupling is consistent with satellite observations of the close
association between magnetic field aligned currents, parallel electric
fields, inverted *V* structures and plasma pressure inhomogeneities
in the magnetosphere and related geomagnetic micropulsations ( Lundin and
Evans, 1985; Chmyrev *et al.,* 1985 ; Stasiewicz, 1985; Bosqued *et
al*., 1986).

**Conclusion**

The universal period
doubling route to chaos is the growth phenomena of a dynamic unified scale
invariant atmospheric eddy continuum from turbulence scale at the planetary
surface with inherent steady state ordered energy flow between the component
eddies and the continuum. The bi-directional energy flow in the planetary
eddy continuum is manifested as various tropospheric, ionospheric and magnetospheric
phenomena in a continuous chain of individual perturbation events in a
space-time continuum which is super symmetric being the fusion of the individual
component eddy symmetries. The bi-directional energy flow in the unified
planetary atmospheric eddy continuum is the coupling mechanism of upper
atmosphere to the lower atmosphere and occurs in the form of a vertical
global aerosol current and the accompanying geomagnetic ** H **component.
Since the time scale for the downward transport of extra-terrestrial energy
input is in the order of several days, global geomagnetic field variations
can serve as precursor signals to weather/climate change. The solar modulation
of

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