The data and results
that we will be discussing come largely from
experiments conducted at the Kennedy Space Center
(KSC). A large (15 km x 25 km) network of
electric field mills is operating at KSC to identify
and warn of thunderstorm and lightning hazards.
The pre-1995 configuration of the field mill network
is shown in the figure below (source of this and the
following three figures: J.M.
Livingston
and
E.P.
Krider,
"Electric
Fields
Produced
by
Florida
Thunderstorms,"
J. Geophys. Res., 83, 385-401, 1978). The
network was upgraded in 1995.
The network that was operating up to 1995 had 0.1 second time resolution. That is fast enough to resolve a lightning flash, but not the individual return strokes that make up cloud to ground flashes. The dynamic range was -15 kV/m to +15 kV/m and E field signals were digitized with 30 V/m accuracy. The overall accuracy of an individual field mill was about 10%.
Examples of fields recorded during 6 small storms. Storms in this category lasted from 35 up to 85 minutes. Individual storms produced 16 to 82 discharges. The maximum flashing rate during a small storm is 1 flash/minute.
A single example of a large storm E field record is shown below
Storms like this are often broken into initial, very active, and end-of-storm-oscillation portions. Note the very slow but large amplitude oscillations in the final EOSO portion.
Large storms in the Livingston and Krider study had durations ranging from 75 to 265 minutes, produced 515 to 1212 discharges, and maintained flashing rates of 5 to 10 flashes per minute for 50 to 90 minutes. Number of flashes per 5 minute interval in a representative large storm are shown in the histogram below.
It turns out we really won't be analyzing electric fields measured at the ground, rather the field changes, ΔE. The figure below explains why this is the case.
Fields measured at the ground usually have lower amplitudes than fields measured just a 100 or 200 meters above the ground. Fields at the ground probably wouldn't exceed 10 kV/m; fields just a few hundred meters above the ground could be several times larger. The field changes measured at the ground and aloft are the same.
As the field at the ground begins to build after a lightning discharge, corona discharge from pointed objects and vegetation "sprays" space charge into the air above the ground. This limits the amplitudes of fields seen at the ground and affects the shape of the field recovery between flashes. We can't really get an accurate measurement of the thunderstorm field at the ground. You can, however, get an accurate measurement of the field change at the ground (it occurs so quickly that space charge can't be created or move quickly enough to affect the field change value).
The network that was operating up to 1995 had 0.1 second time resolution. That is fast enough to resolve a lightning flash, but not the individual return strokes that make up cloud to ground flashes. The dynamic range was -15 kV/m to +15 kV/m and E field signals were digitized with 30 V/m accuracy. The overall accuracy of an individual field mill was about 10%.
Examples of fields recorded during 6 small storms. Storms in this category lasted from 35 up to 85 minutes. Individual storms produced 16 to 82 discharges. The maximum flashing rate during a small storm is 1 flash/minute.
A single example of a large storm E field record is shown below
Storms like this are often broken into initial, very active, and end-of-storm-oscillation portions. Note the very slow but large amplitude oscillations in the final EOSO portion.
Large storms in the Livingston and Krider study had durations ranging from 75 to 265 minutes, produced 515 to 1212 discharges, and maintained flashing rates of 5 to 10 flashes per minute for 50 to 90 minutes. Number of flashes per 5 minute interval in a representative large storm are shown in the histogram below.
It turns out we really won't be analyzing electric fields measured at the ground, rather the field changes, ΔE. The figure below explains why this is the case.
Fields measured at the ground usually have lower amplitudes than fields measured just a 100 or 200 meters above the ground. Fields at the ground probably wouldn't exceed 10 kV/m; fields just a few hundred meters above the ground could be several times larger. The field changes measured at the ground and aloft are the same.
As the field at the ground begins to build after a lightning discharge, corona discharge from pointed objects and vegetation "sprays" space charge into the air above the ground. This limits the amplitudes of fields seen at the ground and affects the shape of the field recovery between flashes. We can't really get an accurate measurement of the thunderstorm field at the ground. You can, however, get an accurate measurement of the field change at the ground (it occurs so quickly that space charge can't be created or move quickly enough to affect the field change value).
Measured field
change values as a function of distance
(source: E.A.
Jacobson
and
E.P.
Krider,
"Electrostatic
Field
Changes
Produced
by
Florida
Lightning," J. Atmos. Sci., 33, 103-117,
1976). Note that small field
change values are sometimes observed very
close to a discharge. We'll come back to
this observation later in today's notes.
Now lets start to look at what can be done when field change measurements are made at multiple locations on the ground.
We'll consider the simplest model of a
cloud-to-ground discharge and assume that the
charge neutralized by the flash comes from a
uniform sphere of charge in the cloud.
You can treat this as a single point charge
(Point 1). Our objective will be to use
the delta E measurements to determine the
location (x, y, and z coordinates) and
magntitude of the neutralized charge (ΔQ).
We show the location of one of the field mill sites in the figure. At that location we will have a measurement of the field change, ΔEmi. We can also calculate the field change that the charge neutralized at Point 1 would produce at Point 2, the location of the ith field mill site. The expression for this calculated field change is shown below.
We're trying to determine ΔQ, x, y, and z. How can we calculate ΔEci if we don't know what they are? We make an initial guess about the location and the amount of charge neutralized during the lightning discharge. And we have field change measurements and can calculate field changes at the other field mill sites. We can adjust the values of x, y, z, and ΔQ until the chi-squared function below is minimized. That will give us our best estimate of ΔQ and its location.
Next we'll look at some results (source: the Jacobson and Krider, 1976 paper cited earlier)
This first histogram gives solutions for ΔQ, the (negative) charge carried to ground in 70 cloud to ground discharges.
The next histogram shows that this charge was largely found between 6 and 9 or 10 km altitude.
Note that this corresponds to a -10o to -30o or -35o C temperature range (the -10o to -30o C range is highlighted above).
Finally the figure below shows that 75% of cloud-to-ground discharges strike the ground at a distance, D, of 5 km (3 miles) or less from the center of the charge neutralized by the flash. 95% of the discharges strike the ground within 8 km (5 miles) of the charge center. The distance D is defined in the figure below at right.
You would generally expect the field change amplitude to get larger as you get closer to a storm. We pointed out earlier however that the field amplitude is sometimes surprisingly small when you are very close to a storm. The field change may also switch polarity.
Now lets start to look at what can be done when field change measurements are made at multiple locations on the ground.
We show the location of one of the field mill sites in the figure. At that location we will have a measurement of the field change, ΔEmi. We can also calculate the field change that the charge neutralized at Point 1 would produce at Point 2, the location of the ith field mill site. The expression for this calculated field change is shown below.
We're trying to determine ΔQ, x, y, and z. How can we calculate ΔEci if we don't know what they are? We make an initial guess about the location and the amount of charge neutralized during the lightning discharge. And we have field change measurements and can calculate field changes at the other field mill sites. We can adjust the values of x, y, z, and ΔQ until the chi-squared function below is minimized. That will give us our best estimate of ΔQ and its location.
Next we'll look at some results (source: the Jacobson and Krider, 1976 paper cited earlier)
This first histogram gives solutions for ΔQ, the (negative) charge carried to ground in 70 cloud to ground discharges.
The next histogram shows that this charge was largely found between 6 and 9 or 10 km altitude.
Note that this corresponds to a -10o to -30o or -35o C temperature range (the -10o to -30o C range is highlighted above).
Finally the figure below shows that 75% of cloud-to-ground discharges strike the ground at a distance, D, of 5 km (3 miles) or less from the center of the charge neutralized by the flash. 95% of the discharges strike the ground within 8 km (5 miles) of the charge center. The distance D is defined in the figure below at right.
 |
 |
You would generally expect the field change amplitude to get larger as you get closer to a storm. We pointed out earlier however that the field amplitude is sometimes surprisingly small when you are very close to a storm. The field change may also switch polarity.
These
observations suggest that a lower volume
of positive charge might be involved in
cloud-to-ground discharges. This led
to the development of a 2 charge model,
illustrated below.
This
is the most general form of the two
charge model - the two charges can
have different magnitudes and can have
completely different locations in
space. A variation on this is
the point dipole model where the two
charges are of equal amplitude but
opposite polarity. Another model
assumes the two charges are aligned
vertically. The calculated field
change expression now contains 8
unknowns (ΔQ1,
x1,
y1,
z1,
ΔQ2,
x2,
y2,
and z2).
Again you use pairs of measured and
calculated fields and minimize a
chi-squared function to determine the
optimal solution for these charge and
location variables.
The next two figures shows some of the results obtained with this arbitrary 2 charge model (source: M.J. Murphy, The Electrification of Florida Thunderstorms, PhD Dissertation, Univ. of Az., 1996)
The next two figures shows some of the results obtained with this arbitrary 2 charge model (source: M.J. Murphy, The Electrification of Florida Thunderstorms, PhD Dissertation, Univ. of Az., 1996)
The
circles indicate charge
neutralized during lightning
discharges, time and altitude are
plotted along the horizontal and
vertical axes, respectively.
Cross hatched circles are positive
charge, open circles are negative
charge. The radius of the
circle is proportional to the
amount of charge neutralized.
Both intracloud and cloud to ground discharges were occurring during this storm. An example of each is shown. Intracloud discharges involve positive charge in the main positive charge center located in the upper portion of the thundercloud and negative charge in the main negative charge center in the middle of the cloud. Cloud-to-ground discharges neutralize negative charge in the middle of the cloud and almost always involve some positive charge in one of the lower positive charge centers. The vertical dotted lines at the bottom edge of the figure indicate cloud-to-ground discharges detected and located by the National Lightning Detection Network.
The next figure is from a little more active thunderstorm cell.
There seems to be a tendency for the amounts of charge neutralized in discharges to increase with time (larger diameter circles toward the end of the storm). The altitudes of the positive charges neutralized in intracloud discharges seem to move to higher altitudes in the middle and later portions of the storms.
The chi-squared procedure for determining charge center locations and charge magnitudes using multi-station field change measurements has also be used with slow E field antenna systems. Slow E records have faster time resolution and can accurately record the field changes produced by the separate return strokes in a cloud to ground flash. The results we looked at above were derived from field mill records and were an integration of all the processes that occur during a flash.
A photograph of one of the slow E field antennas is shown below at left. A schematic diagram of the antenna electronics is shown at right. The slow E network that we will be discussing was built and operated by researchers from the New Mexico Institute of Mining and Technology (P.R. Krehbiel, M. Brook, and R.A. McCrory, "An Analysis of the Charge Structure of Lightning Discharges to Ground," J. Geophys. Res., 84, 2432-2456, 1979).
The antenna sensor plate is
mounted about 1 m above the ground
and is surrounded by a culvert
(probably to keep cattle and
wildlife away from the
antenna. The decay time
constant of the integrating
electronics was 10 seconds.
It is worth pointing out that,
because the antenna plate is not
mounted flush with the ground, its
effective area will be greater
than its geometric area.
The effective crossectional
area of a sensor plate positioned
above the ground is greater than
its geometrical crossection.
Some of the E field lines that
wouldn't strike a plate mounted
flush with the ground curl around
and strike the sides or bottom of
a plate positioned above the
ground. The effective area
would need to be determined by
calibration.
The antenna network was installed near Socorro, New Mexico.
An example of a CG flash slow E
field record is shown in the
figure below. Six return
strokes have been identified.
A stepped leader field change can be clearly see on several of the records and has been highlighted in yellow. The slow field change that follows the last return stroke is caused by a continuing current and has been highlighted in pink.
The figure below shows locations of the charges neutralized by the separate return stroke in 4 cloud-to-ground flashes. Flash 9 has been highlighted because those are the charge locations determined using the slow E field data shown above. Charge tapped by the continuing current that followed the 6th return stroke in Flash 9 has been highlighted in pink.
Both intracloud and cloud to ground discharges were occurring during this storm. An example of each is shown. Intracloud discharges involve positive charge in the main positive charge center located in the upper portion of the thundercloud and negative charge in the main negative charge center in the middle of the cloud. Cloud-to-ground discharges neutralize negative charge in the middle of the cloud and almost always involve some positive charge in one of the lower positive charge centers. The vertical dotted lines at the bottom edge of the figure indicate cloud-to-ground discharges detected and located by the National Lightning Detection Network.
The next figure is from a little more active thunderstorm cell.
There seems to be a tendency for the amounts of charge neutralized in discharges to increase with time (larger diameter circles toward the end of the storm). The altitudes of the positive charges neutralized in intracloud discharges seem to move to higher altitudes in the middle and later portions of the storms.
The chi-squared procedure for determining charge center locations and charge magnitudes using multi-station field change measurements has also be used with slow E field antenna systems. Slow E records have faster time resolution and can accurately record the field changes produced by the separate return strokes in a cloud to ground flash. The results we looked at above were derived from field mill records and were an integration of all the processes that occur during a flash.
A photograph of one of the slow E field antennas is shown below at left. A schematic diagram of the antenna electronics is shown at right. The slow E network that we will be discussing was built and operated by researchers from the New Mexico Institute of Mining and Technology (P.R. Krehbiel, M. Brook, and R.A. McCrory, "An Analysis of the Charge Structure of Lightning Discharges to Ground," J. Geophys. Res., 84, 2432-2456, 1979).
The antenna network was installed near Socorro, New Mexico.
A stepped leader field change can be clearly see on several of the records and has been highlighted in yellow. The slow field change that follows the last return stroke is caused by a continuing current and has been highlighted in pink.
The figure below shows locations of the charges neutralized by the separate return stroke in 4 cloud-to-ground flashes. Flash 9 has been highlighted because those are the charge locations determined using the slow E field data shown above. Charge tapped by the continuing current that followed the 6th return stroke in Flash 9 has been highlighted in pink.
In
each case successive return
strokes tap separate volumes
of charge that are further and
further away from the staring
location.