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.

The atmospheric boundary layer (

(1)

where ** W** and

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 ** w_{*}** is
the unidirectional turbulent eddy acceleration and

(3)

** k = 0.4** for

(4)

The rising large
eddy gets progressively diluted by vertical mixing due to the turbulent
eddy fluctuations and a fraction ** f** of surface air which reaches
the normalized height

From Eqs. (2) and (3)

(5)

*W = w _{*} f z*

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

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 ** -2** . The universal
scale invariant

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

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

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

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

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

*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

(8)

** a** is therefore
equal to

Let

(9)

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

*s =s _{*}
f*

(10)

*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

magnetism and atmospheric electricity.

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