The next several figures show measurements of fair weather air conductivity, electric field, and current density made during a 1978 field experiment in Wyoming.  Simultaneous measurements were made with a variety of different instruments from perhaps half a dozen different research groups.  Instruments were carried up to about 30 km altitude by balloon and measurements were made on the ascent and often during the descent.  You'll find a link to the full article at the end of today's notes.

The list below gives you an idea of the electrical parameters that were measured and the various types of sensors that were used.

 

Measurements of conductivity versus altitude made on two different days are shown in two graphs below.


Conductivity values range from about 5 x 10-14 mhos/m at 2 km or so above the ground to about 1000 times higher than that near 30 km.  Note that conductivity is plotted on the x-axis on a logarithmic scale.  The 10 - 30 km portion of the graph appears pretty linear implying conductivity is increasing exponentially with altitude. 


The conductivity values are from just the positively charged small ions.  The notation "GC" in the figure refers to "Gerdien Condenser."  The cylindrical capacitor discussed in the last lecture would be an example of a Gerdien condenser type instrument.  Conductivity was estimated using the Isignal/V slope method described in our last lecture (σ is used in the article instead of λ).



All of the measurements are in good agreement with the exception of the relaxation time method.  This is just the decay time constant we derived in a previous lecture.

 

A second set of conductivity measurements.  These include both positive and negative small ions.

 

The next two plots show measurements of electric field versus altitude (the same two plots were on the 2nd homework assignment).



E field values decrease from a few 10s of volts/meter 2 or 3 km above the ground to less than 1 V/m near 30 km (note: the x-axis values are, from left to right, 0.1, 1.0, 10 and 100 V/m).

 

The next plot shows the vertical profile of current density, Jz.  Measurements from two different days are plotted together. 


Note first of all that current density does stays fairly constant with altitude something we expect under steady state conditions (the x-axis labels, from left to right, are 0.1, 1.0 and 10 pA/m2). 

The yellow curve is the product of electric field and positive small ion conductivity, all the others are measurements of Jz.  You would expect the measured Jz (which includes both positive and negative charge carriers) to to be roughly twice the positive conductivity times electric field, but it isn't. 

The problem appears to have been corrected in the plot below which is a reanalysis of the Wyoming data.  The plotted points are conductivity (positive and negative polarity) times measured electric field.  The plotted values cluster around a value of about 2.5 pA/m2 (note again how uniform Jz is with altitude).  Measured Jz was about twice this, about 5.1 pA/m2.


The next graph summarizes measurements from a different field experiment conducted in the North Atlantic ocean.

The plot shows vertical profiles of E field (highlighted in blue), measured positive and negative conductivities (green), and the calculated current density (in yellow, the product of positive and negative conductivity and measured electric field).  The calculated current density values are clustered around 1.25 pA/m2, the measured total current density was about twice that, 2.35 pA/m2.


The last two figures above from W. Gringel, J.M. Rosen, ande D.J. Hofmann, "Electrical Structure from 0 to 30 km Kilometers," Ch. 12 in The Earth's Electrical Environment, National Academy Press, 1986. (available online at www.nap.edu/books/0309036801/html/)


References:
J.M. Rosen, D.J. Hofmann, W. Gringel, J. Berlinski, S. Michnowski, Y. Morita, T. Ogawa, and D. Olson, "Results of an International Workshop on Atmospheric Electrical Measurements, "J. Geophys. Res., 87, 1210-1227, 1982.