====== Lightning discharge ======
original source(([[http://en.blitzortung.org/Compendium/Documentations/Documentation_2014-05-11_Red_PCB_10.4_PCB_12.3_PCB_13.1_PCB_14.1.pdf|Documentation System RED]], chapter 3.1))

How lightning initially forms is still a matter of debate((H.D. Betz, U. Schumann, and P. Laroche (Eds.) Lightning: Principles, Instruments and Applications. Springer Verlag, 2009.)). Scientists have studied root causes
ranging from atmospheric perturbations (wind, humidity, friction, and atmospheric pressure) to the
impact of solar wind and accumulation of charged solar particles. Ice inside a cloud is thought to be
a key element in lightning development, and may cause a forcible separation of positive and negative
charges within the cloud, thus assisting in the formation of lightning. It was not obvious, that lightning
deals with electricity, since the electric current does not flow through the air. This, on June 10th 1752,
Benjamin Franklin flies a kite during a thunderstorm and collects a charge in a Leyden jar when the
kite is struck by lightning, enabling him to demonstrate the electrical nature of lightning. He also
invented the lightning rod, used to protect buildings and ships.

{{:en:detection:franklin.png?700|}}

A lightning discharge emits radio frequency energy over a wide range of frequencies. When
high currents occur in previously ionized channels during cloud-to-ground flashes, the most powerful emissions occur in the VLF range. VLF (very low frequency) refers to radio frequencies in the range
of 3 kHz to 30 kHz. An essential advantage of low frequencies in contrast to higher frequencies is
the property that these signals are propagated over thousands of kilometers by reflections from the
ionosphere and the ground. In general, a lightning discharge generates several short duration pulses
running between a storm cloud and the ground, or between or within storm clouds. The current flow
generates an electric field parallel to the current flow, and a corresponding magnetic field perpendicular to the electric field.

===== Receiving a lightning signal =====

Waves with a frequency between 3 kHz and 30 kHz have a length between 100 km and 10 km. A
suitable antenna for these frequencies is a small loop antenna with size of less than 1/10000 of the
wavelength in circumference. Small loops are also called magnetic loops, because they are more
sensitive to the magnetic component of the electromagnetic wave, and less sensitive to near electric
field noises when properly shielded. If the loop is small with respect to the wavelength, the current
around the antenna is nearly completely in phase. Therefore, waves approaching in the plane of the
loop will cancel, and waves in the axis perpendicular to the plane of the loop will be strongest. This
property changes if the loop becomes larger.

{{:en:detection:rahmenantenne_1.jpg?300|}}

The electric field of the radio waves emitted by cloud-to-ground lightning discharges is mainly
oriented vertically, and thus the magnetic field is oriented horizontally. To cover all directions (all-
around 360 degree) it is advisable to use more than one loop. A suitable solution can be obtained by
two orthogonal crossed loops as they are used for a direction finding system.

The electromagnetic signals of lightning discharges are not waves of a fixed frequency. The signals
have more or less the form of an impulse and thus emits waves over a wide range of frequencies. Every
of these impulses is unique and looks different. To measure the time of arrival of a lightning discharge,
we need a wide-band receiving system, and not a tuned system. The antenna should be large to get a
high voltage caused by the change of the electromagnetic field. If the loop consists of more than one
winding, the wire placed side by side forms a capacitance.

However, the unavoidable own resonance frequency of a loop should be as high as possible such
that we can easily suppress these frequencies by a low-pass filter. Figure 5 shows to the left a signal
received by two equal sized untuned loops antennas. These loops have no additional tuning capacitor.
The resonance frequency of the antenna is approximately at 1000 kHz (= 1 MHz). The used amplifier
reduces frequencies of 1000 kHz by -72 dB (=4000 times). To the right of Figure 5, Loop B is con-
nected to a parallel tuning capacitor of 1 µF. Now, the tuned frequency is the antenna is approximately
10 kHz. Since lightning impulses often contain a lot of energy at 10 kHz, the tuned loop antenna only
outputs unusable uniform waves of 10 kHz. This shows that it is very important to use a pure loop
without any parallel capacitor.

<note important>
Hint: Please avoid any additional tuning capacitor!
</note>

{{:en:detection:spektrum.jpg?400|}}

Figure 4: A spectrogram of the signal received by a 35 cm ferrite rod antenna. The signal was
recorded by a Creative Professional E-MU 0202 sound card with a sampling frequency of 192 kHz.
The spectrogram is made by Spectrum Lab. Vertical lines shows radio transmissions for special
purpose, and do not affect our reception.

{{:en:detection:signal_1.jpg?400|}} {{:en:detection:signal_2.jpg?400|}}

Figure 5: To the left, a signal received by two loop antennas without tuning capacitors, to the right,
antenna B is tuned to approximately 10 kHz. This signal cannot be used for time measurement.

===== Time-of-Arrival method =====

The TOA lightning location technique is based on the computations of hyperbolic curves. The emitted
radio signal of a lightning discharge is traveling through the air with the speed of light. This
is approximately 300000 kilometers per second, or equivalently, 300 meters per microsecond. Each
received signal gets a time stamp. Let //tA(s)// be the time stamp for signal //s// from station A. Time
stamp //tA(s)// is the Coordinated Universal Time (abbreviated UTC) in microseconds with an accuracy
of ±1µs. The difference of two time stamps for the same signal received by two different stations
and the positions of these two stations define a hyperbolic curve. Let //dA(p)// be the distance of a point
//p// to station A in meter. Then the hyperbolic curve for signal //s//, is the set of all positions //p// whose
distance difference //dA(p) − dB(p)// in meter corresponds to the time stamp difference //tA(s) − tB(s)//
in microseconds converted by the speed of light into meter. That is,

//dA(p) − dB(p) = (tA(s) − tB(s)) * 300.//

{{:en:detection:tworeceivers.png?400|}}

Figure 6: The receiver to the left receives the lightning signal 60µs later than the receiver to the right,
because the lightning discharge is 18 kilometers more far away from the receiver to the left than from
the receiver to the right.

The source of the signal has to be somewhere on this hyperbolic curve. The intersection point of
three or more such hyperbolic curves defines the unique location of the source of the radio signal, see
Figure 7. The computed position is then be assumed to be the location of the lightning discharge. At
least 4 sites not on a line are needed to define always a unique intersection point. With more than four
receiving sstations reporting a time stamp for the same signal there is some redundant information
available to improve the accuracy and to verify the performance.

{{:en:detection:hyperboliccurves.png?400|}}

Figure 7: Three hyperbolic curves defined by the three time differences //tB(s) − tA(s)//, //tC(s) − tA(s)//,
and //tD(s) − tA(s)// of four sites //A//, //B//, //C//, and //D// (the green squares). The intersection of all three
curves uniquely defines the location of the source of the radio signal (the white dot). The curves have
a width corresponding to a tolerance of ±5µs. That is, the white area for signal s received by station
A and B is the set of all points p for which

//(tA(s) − tB(s)) * 300 − 5 ≤ dA(p) − dB(p) ≤ (tA(s) − tB(s)) * 300 + 5//.

A time difference of ±100 microseconds corresponds to a distance difference of ±30 kilometers.
That is, if site //A// receives the same signal 100 microseconds earlier than site //B//, the corresponding
hyperbolic curve is defined by the set of all points that are 30 kilometers near to site //A// than to site //B//.
Assume the time stamps have an accuracy of ±1µs and there are four sites arranged such that their
positions define a square. If the signal source is exactly in the middle of the square, then the deviation
of the computed position to the real source of the signal is greater than ±300m * √2 = 424m. It
can be much greater if the source of the signal is outside the square, see Figure 8. The argumentation
of some commercial providers that their system has an accuracy of ±300 meters, because the time
stamp has an accuracy of ±1µs, is a naive fallacy.

The main challenge of a TOA lightning location system is to assign the received signal a unique
characteristic time stamp. This is not easy, because the outline of the signal changes when it travels
over long distances. One way to handle different signal forms, is to compute a time of group arrival,
see((R.L. Dowden and J.B. Brundell and C.J. Rodger. VLF lightning location by time of group
arrival (TOGA) at multiple sites. Journal of Atmospheric and Solar-Terrestrial Physics,
64(7):817-830, 2002.)). However, if the time stamps are not consistently assigned, the hyperbolic curves do not
intersect in a common intersection point. A collection of several nice papers about lightning detection
can be found in((H.D. Betz, U. Schumann, and P. Laroche (Eds.) Lightning: Principles, Instruments and
Applications. Springer Verlag, 2009.)).

{{:en:detection:deviations.png?400|}}

Figure 8: The deviations for an accuracy of ±1µs for different cut angles

The computations at our server are carried out in two steps. In the first step a starting point is computed
using the method from((W.J. Koshak and R.J. Solakiewicz. TOA Lightning Location Retrieval on Spherical and
Oblate Spheroidal Earth Geometries. Journal of Atmospheric and Oceanic Technology,
18(2):187-199, 2001.)) applied to the first 4 time stamps. After that a numerical method
is used to minimize the sum of all squared distances to the hyperbolic curves. All our computations
use spherical coordinates.

===== The Blitzortung.org network =====

{{:en:detection:lightning.jpg?400|}}\\
Figure 9: Some lightning discharges in the atmosphere, (c) Bernd März

The lightning location network Blitzortung.org consists of several VLF lightning receiver sites
and one central processing server for each larger region. The receiver sites transmit their data in short
time intervals over the Internet to our server. Every data sentence contains the precise time of arrival
of the received lightning strike impulse ("sferic") and the geographic position of the receiver site. With
this information from all receiver sites the exact positions of the discharges are computed. The sferic
positions are made available in raw format to all users that transmit their data to our server. The users
can use the raw data for all non-commercial purposes. The lightning activities of the last two hours
are displayed at Blitzortung.org on several public maps recomputed every minute.

{{:en:detection:usa_20130920_0900_24h.png?400|}}\\
Figure 10: A lightning map of USA from [[http://blitzortung.org|Blitzortung.org]]

Note that it is not possible to compute positions or at least accurate directions with the data from
one station. We need the data of several stations (at least four stations) to compute strike positions.
There is currently no software that enables you to set up a connection with other sites like the LR
software of LightningRadar.net for the direction finding system. The computation of strike positions
is only done by one of our computing servers.

==== Accuracy ====

Figure 11, 12, and 13 show a comparison of the positions computed by Blitzortung.org and "BLIDS"
over Germany, Belgium, and Poland. BLIDS is a lightning information system in Germany. Figure
14 shows the used color code for the age of the discharges.

{{:en:detection:blids1.jpg?400|}}\\
Figure 11: A comparison of the positions computed by blitzortung.org (the white framed colored squares) and BLIDS (the colored squares) in Germany

{{:en:detection:blids2.jpg?400|}}\\
Figure 12: A comparison of the positions computed by blitzortung.org (the white framed colored squares) and BLIDS (the colored squares) over Belgium, the Netherlands, and Luxembourg

{{:en:detection:blids3.jpg?400|}}\\
Figure 13: A comparison of the positions computed by blitzortung.org (the white framed colored
squares) and BLIDS (the colored squares) over Poland

| {{:en:detection:blids_magenta.png?40|}} | {{:en:detection:blids_purple.png?40|}} | {{:en:detection:blids_blue.png?40|}} | {{:en:detection:blids_turquoise.png?40|}} | {{:en:detection:blids_green.png?40|}} | {{:en:detection:blids_yellow.png?40|}} | {{:en:detection:blids_orange.png?40|}} | {{:en:detection:blids_red.png?40|}} |
| 120 - 105 | 105 - 90 | 90 - 75 | 75 - 60 | 60 - 45 | 45 - 30 | 30 - 15 | 15 - 0 |\\
Figure 14: The BLIDS color code for the age of the lightning discharges in minutes