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• ## A heavy mathematical discussion of SSTs and hurricanes

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• This is a continuation on the theme of conductivity impacts on tropical storms, with, for instance, gravity waves equating to out gassings of CO2 and then
Message 1 of 1 , Apr 24, 2005
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This is a continuation on the theme of conductivity impacts on
tropical storms, with, for instance, gravity waves equating to out
gassings of CO2 and then conductivity dynamics that follow. These
extremely heavy math focuses only on SSTs.

I recently did a crude calculation with my voltmeter, outdoor
thermometer, salt from a shaker, and a coffee cup. I got about (with
the unmeasured dash of salt) about a percent decrease in resistance
with each degree increase in temperature.

If you want it exactly it will cost you about \$600+:

http://www.fondriest.com/products/ysi30.htm

My experiment was not too far from the texts. Try:

http://www.thermorussell.com/techcond.htm

They give 2.12% / degC.

The fun starts when you start putting salt in your beer and shaking
it and trying conductivity readings on the surface of your beer--but
I will leave that for Friday night. Of course, the amount of salt is
important, too, and why you will get slightly different numbers of
try this at home--unless you have one of those floaters I used to
have with my ocean fish tanks and we can be on the same specific
gravity page.

Please consider, anyway, the following VERY carefully. The CHINA
paper SHOWS that the with kvolt transients you start to see changes
in how the ion ice forms. See it:

http://www.ichmt.org/abstracts/Vim-01/abstracts/04-01.pdf

Quote:

"The effects of electric field on ice crystal growth had been
numerically discussed by Scishcheve and Kusalike6-7. They announced
that the strength of an electric field able to change the ice lattice
from normal ice(Ih) to cubic ice (Ic) should be at least 10 to the
5th kV/m However, the strength of the electric field used in our
experiments was only 1/400 of the 10 to the 5th kV/m . . ."

Now, check this out:

http://www.aoml.noaa.gov/hrd/tcfaq/G10.htm

Quote:

Consistent with this, Burke et al. [1992] has reported the detection
of keV electrons and large electric field transients above a
hurricane. These various observations all suggest that what is
occurring at great depths in the ocean may couple to the ionosphere.
The coupling mechanisms was said by them not to be well understood,
but it seems probable that "capacitive coupling" through the
displacement current my drive conduction currents within the
ionosphere [Hale and Baginski, 1987].

ke Volts = 10 to 9 power or 1000 kvolts/meter.

By my calculations from above the electric field used in the China
experiment was 250 kV/m.

So you are certainly in the voltage range where you can OBSERVE the
microphysics changes in an ion solution with the same pH as rainwater.

I am going to just talk about power.

Electrical power is measured in watts. One watt equals one (J) joule
per second. A joule is the SI unit of work or energy, defined to be
the work done by a force of one newton acting to move an object
through a distance of one meter in the direction in which the force
is applied. Equivalently, since kinetic energy is one half the mass
times the square of the velocity, one joule is the kinetic energy of
a mass of two kilograms moving at a velocity of 1 m/s. In an
electrical system power (P) is equal to the voltage multiplied by the
current. Since we are taking about a forcing moving an object at a
distance, then we can talk about, mathematically, about moving an
accumulation of charges a distance as the eye of the hurricane moves.

P = VI

By ohm's law

I = V / R can be restated as V = I R

Now you can substitute the equation for V into the other equation:

P = V I substituting for V we get P = IR I, or

P = I2R

Okay? This is basic stuff. We can assume that the resistance is
constant for this problem, and the current is expressed, ultimately,
in electrons.

Now. Again. Picture a hurricane and extreme accumulations of
relatively positive charges above the eye in the ionosphere (not the
clouds, please, for God's sake, don't confuse the action on the
clouds with where the actual currents are). These charges COUPLE with
the ocean where the skin of the ocean has relatively negative
charges. This is a static field and in that static field microphysics
of clouds are impacted and barotropic is organized. This organization
of clouds cannot occur well outside of the eye because water carries
a strong dielectric constant and interferes with the ability of the
coupling, the opposites attracting by static field, to occur. With me
so far?

Okay. Now the hurricane MOVES. And so for there to be a static field
it must go 'around' the cloud. Now appreciate that these tropical
storm eyes are sometimes 200 miles across, and, say, a typical cat 5
in the Atlantic will have a 25 mile diameter eye. So as the storm
moves, say, at 10 MPH, the static field isn't completely covered by
water, but it does move. As it moves, so must the static field in
order for the microphysics impact to remain coherent.

Now, now matter what the pathway the charges move, it takes POWER to
move them.

Okay?

Power is required. Like the economist once said, there is no free
lunch.

And the more resistance and the greater the field we are trying to
move, the more power it will take to move these charges.

Work or power is required to alter the cloud microphysics, too.

But I am just focused on the ocean surface for this time. And
ignoring the out gassing and conductivity patterns therefrom. And I
could talk about resistance in the ionosphere as well, and that would
apply with respect to what I am talking about with the equinox. But
for the moment, I am just looking at temperature of the oceans, which
we have already seen a percentage difference per degree and if we are
talking about 72 to 82 degrees, that's a 10 percent drop in power
requirement to keep the static field going that organizes cloud
microphysics, assuming all other things being equal.

We are talking about capacitive couplings between ocean and
ionosphere. The charges are not moving from point a 10 feet below the
ocean to points 1000 feet below the surface of the ocean. They are
moving between conductive points on the surface of the ocean and
coupling with conductive elements in the ionosphere. Current CAN'T
FLOW significantly between ocean and ionosphere--what is coupling
these two places is a magnetic field. A static field. You know,
opposing charges attract. That attraction is due to a magnetic field.
In between these fields in the air is water (clouds) which has
dielectric meaning to this coupling. Now, this static field MOVES. As
it moves, it will move along, again, the surface of the ocean. It
moves with visible effect. Indeed, there is both the behavior of
the 'eye' as well as internally, the mesovortices, which are
comprised of zones of water and less water, as well as transients of
these kevolt accumulations, but relatively cloud free to 'be' an eye.
So there is microphysics impacts in the eye generally and inside the
eye specifically, and this gets to be important when, say, you are
talking about a storm like Andrew with 5 mesovortices . . .

Now imagine that there is an increase in the resistance of the oceans-
-such as a decrease in ocean temperature. That prevents the movement
or coupling from further occurring.

Consider this picture of the Pacific ocean in infra red and the
clouds there:

http://www.weather.unisys.com/hurricane/sat_ir_p.gif

this picture, even from a common sense perspective, indicates that
the tropical ITCZ and the storm to the north of it in the mid Pacific
operate under different rules of thermodynamics and microphysics--and
indeed the electrical fields imposed on the cloud microphysics ARE
different for the tropics and the mid lattitude storms like this.

In sum.

P = I2R

Power equals current squared times resistance. Current is expressed
in electrons. Resistance as we have seen is a percentage of
temperature.

The dipole static field with the huge accumulations of electrons and
positive ions in a hurricane eye will have to be moved with the
hurricane in order to aid organization. That movement will be
substantially along the skin of the surface because that is where the
coupling occurs. That movement at a distance requires POWER. That
power requirement is proportionate with resistance. It will take, to
maintain status quo of a hurricane, about 10 percent more power to
organize a hurricane--as it was, for each drop in degrees F. in SSTs.

I will make an assumption is that there are an infinite
number of current paths from one area on the surface of the ocean
charged by the static field between ocean and ionosphere, so no
matter how large the resistances in each 'wire', the net current will
flow not on the surface but below it, negating any degree change in
resistance that SSTs bring. So let's take that logic and see where it
goes.

To solve this problem, we first need to find what is called
equivalent resistance. This is the resistance for the sum of all
these 'wires' that DED is saying exist, providing a current path that
avoids the surface resistance. Equivalent resistance can be found if
you know the individual resistance values and the source voltage.

1/Req=1/R1 + 1/R2 + 1/R3+ . . . 1/Rn

This problem is seen better using the reciprocal method:

Req=1 / 1/R1+1/R2+1/R3+ . . . 1/Rn

Now, if we take our assumption that there are infinite number of
current paths, then the denominator becomes infinite and the Req
resistance equals ZERO.

That means that if you have ANY applied voltage, and apply ohm's law
to this Req circuit, than the current is infinite.

How does that check with reality?

It doesn't.

The surface fair weather voltage is 250 volts per meter positive to
ground. What that means is that there is a current of electrons on
the surface moving up to the ionosphere, and that current matches the
input of lightning strikes around the world bring electrons to the
earth in bursts of charges. Now, if there is an ZERO Req, than there
is infinite current to maintain the 250 volts per meter. Is that what
we see? Nope. Not even CLOSE!

That's because static field relationships exist and define the
currents and the application of the resistance on the skin of the
oceans . . . this is all about capacitive couplings, where SSTs
matter electrically.

If you are to take the AVERAGE of the global circuit, it comes out to
be a small voltage, but I am focused on hurricanes, which are
electrically organized events proximate to the conductive tropics and
by my observations proximate to thunderstorm activities. The voltages
required in the China paper to make the microphysics changes have
been OBSERVED. The Bates et all research on Hurricane Felix published
in Nature noted the corresponding change in pp of CO2.

k1 k2 k3
H2O + CO2 <=> H2CO3 <=> H+ + HCO3- <=> 2H+ + CO3.

Increased H+ will drive the equations back toward the right. An
increase in electrons ON THE SURFACE will drive the equation TO THE
LEFT. This is how global CO2 levels MATTER in tropical storm
formations . . . it has an electrical meaning!

There is a potential difference, or a voltage, on the surfaceÂ—which
averages about 100 volts per meter. What that means is if you are
talking about 2 meters above the ocean, the voltage DOUBLES. This is
a vertical measure, not a horizontal measure.

The horizontal measure is current (i) and is measured in meters
squared.

The DYNAMIC field is not straight up and down due to a cloud IN
BETWEEN the ionosphere and ocean SURFACE, will these electrons that
are moved have to experiance the resistance associated with the
surface. The momentary VECTORS of the dynamic field will have a
horizontal aspect and it will 'drag' or cause a voltage (pressure)
movement along the surface.

The confusion is current flow is typically expressed as positive ions
when in this case, you have lighting strikes bringing electrons to
ground and creating a relatively positive charge in the ionosphere.
Strikes occur prodominately in the terrepshere, which means that the
oceans are exposed on average to fair weather. Hurricanes and
tropical storms are relatively strike free, and when strikes do
occur, the electrons are dissapated quickly in the "infinity"
conductive oceans. Yet what remains is the field. That field brings
electrons to the surface attracted to the relative concentrations of
positive ions in the conductive coencentric shell in the ionosphere.

The delta field force that is horizontal can be expressed
mathematically. I will assume for the purposes of this calculation
that we are talking about a hurricane and a moving eyewall. An
eyewall has a significant amount of water and has the shape of a
stadium, and a well developed hurricane is sometimes called as having
a "stadium effect". So the clouds come in at an angle which is
indicative of the fact that there is this horizontal aspect of the
field. I will assume that the cloud level is halfway between ocean
surface and ocean and that water presents such a high dielectric
constant that for practical purposes the field does not exist under
that eyewall and that the coupling runs there from ocean to
ionosphere. Therefore, the delta distance that the cloud wall moves
on the shading edge will be in terms of voltage will be the square
root of sum of the distance from ionosphere to ocean squared minus
the square delta distance. With some calculus and limits math you
could calculate the instantaneous rate.

These hurricane eyes are typically 5-25 miles across in the Atlantic.
The distance between ionosphere and ocean is about 50 miles. If a
hurricane is moving at 25 miles an hour, in one hour the eye is fully
displaced and the electrons that were on the surface of the eye are
now twenty five miles displaced. So you could say that the distance
between ionosphere and ocean is covered every 2 hours.

The reality of an incrementally moving field and that the movement is
in the context of that field forcing which has a horizontal component
in the direction of that movement. Since the movement has both
vertical and horizontal component, the movement of electrons is along
the skin of the oceans and will experience the resistance of the
ocean--in this case we have been discussing how that conductivity is
determined by SSTs.
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