In this lecture we will be looking at some of the ground based techniques used to locate lightning.  We'll start with the magnetic direction finding (MDF) and time of arrival (TOA) techniques currently being used in the National Lightning Detection Network (NLDN).  Click here to see a plot of lightning flash density in the continental U.S. for the period 1997-2010.

The focus there is locating return strokes striking the ground.  Much of the information in this lecture is based on an extensive recent survey of the topic: K.L. Cummins and M.J. Murphy, "An Overview of Lightning Locating Systems: History, Techniques, and Data Uses, With an In-Depth Look at the U.S. NLDN," IEEE Trans. on Electromagnetic Compatibility, 51, 499-518, 2009 (link to a PDF file).

Lightning processes radiate over a broad range of radio frequencies so it might be helpful to start with a a diagram of the relevant portions of the radio frequency spectrum


You can get some appreciation for the variety of lightning RF emissions at different frequencies on the example below with records of slow E field and VHF emission from a cloud-to-ground discharge (adapted from C.O. Hayenga and J. W. Warwick, "Two-Dimensional Interferometric Positions of VHF Lightning Sources", J. Geophys. Res., 86, 7451-7462, 1981).

Large current amplitude processes that propagate along long existing channels such as return stroke and certain intracloud discharges produce VLF and LF radiation.  This is evident on the slow E field record which is dominated by large field changes produced by the four return strokes in this discharge.  The National Lightning Detection Network (NLDN) uses wideband sensors that operate from 10s of kilohertz to a few 100s of kilohertz (to just below the start of the AM radio band at 550 kHz) to locate lightning strikes to ground.  Signals at VLF frequencies can propagate 1000s of kilometers and are used in long range locating systems.



The preliminary breakdown process and stepped leaders radiate particularly strongly at VHF.  Dart leaders, and recoil streamers also radiate strongly at VHF.  If the data above were displayed on a fast time scale we would see that the character of the emissions at VHF differ depending on the type of discharge process.  Leader processes that propagate into unionized air generally produce sequences of narrow isolated pulses (pulse widths of the order of microseconds).  TOA systems are best able to locate the sources of these isolated pulses of radiation.  Other processes such as dart leaders and recoil streamers produce quasi continuous emissions that last for a few milliseconds.  Interferometry is better able to locate the sources of the quasi-continuous emissions. 











VLF signals radiated by a 1st return stroke and a cloud discharge are shown above at left.  Each waveform is shown on slow (top two examples, 100 μs/div) and faster (bottom two signals, 20 μs/div) time scales. 

RF radiation consisting of isolated pulses and a burst of quasi-continuous radiation is shown above at right (adapted from the Cummins and Murphy (2009) paper cited at the start of this lecture).  An isolated pulse is shown on a faster time scale in the lower right panel above (from an online description of the New Mexico Tech Lightning Mapping Array).

A sensor in a magnetic direction finder system uses two orthogonal loop antennas.  One loop is shown below.  A distant lightning strike produces a horizontal magnetic field, B, that passes through the antenna.
 
Faraday's law states that the voltage across the open ends of the loop antenna will be equal to the time rate of change of the flux through the antenna. 


We'll assume that B is uniform across the area of the antenna so that it can be taken out of the integral above.  This voltage signal can be integrated to give a signal that is proportional to B.  An important point to take from this figure is that the output signal from the antenna will depend on the location of the strike with respect to the plane of the antenna (the cosΘ term).  This is developed further in the next several figures.

In the picture above we've assumed an upward moving return stroke current such as would come from a negative cloud-to-ground discharge.  For a positive cloud-to-ground strike, the current would point downward, and the signal from the loop antenna would have the opposite polarity.  Electric fields need to be recorded together with magnetic fields to be able to determine the polarity of the return stroke.  We are also assuming the lightning channel is straight and vertical.



In the figure above we imagine looking down on the loop antenna from above.  Lightning strikes are located north of the antenna in (a), east in (b) and south in (c).  You'd measure a large positive signal coming from the loop in (a), zero signal in (b) because the B field doesn't pass through the antenna (B and the normal vector are perpendicular so their dot product is zero), and a strong negative signal in (c).  We've assumed a negative cloud-to-ground discharge (upward pointing current) in each of these examples.

Next we'll look at how the bearing angle to a lightning strike can be determined using the signals from two orthogonal loops.


We want to be able to determine theta using measurements from a NS loop and EW loop antennas.  We'll look at the output from the NS loop first.

The output signal is proportional to the cosine of the bearing angle. 

The signal from the EW loop is proportional to the sine of the bearing angle.


The bearing angle can be determined by taking the inverse tangent of the ratio of the two loop antenna signals.



Examples of NS signals (uppermost in blue) and EW signals (lower signal in green) that you would expect to see for strikes to the NE, SSE, and WNW of the orthogonal loop antenna.  The square root of the sum of the squares of the two signals gives you the B field amplitude.

Once the distance to the discharge is determined, the B field ampltitude (assumed to be purely radiation field) can be used, together with an assumed return stroke propagation velocity, in the transmission line model to estimate the peak current in the stroke.  You could also use the E field to estimate peak current.  The magnetic direction finding technique is the only one that can provide estimates of peak current amplitudes.

The orthogonal loop antennas used in one of the prototype lightning locating systems was a PVC pipe structure perhaps 8 feet tall.  A picture of that antenna and the next generation antenna, maybe only 2 or 3 feet tall is also shown in "Lightning Direction-Finding Systems for Forest Fire Detection," E.P. Krider, R.C. Noggle, A.E. Pifer, and D.L. Vance, Bull. Am. Meteorol. Soc., 61, 980-986, 1980 (link to a PDF file).  The current sensor is considerably smaller.

Some typical large amplitude cloud discharge and return stroke waveforms are shown below





In the original magnetic direction finding systems the lightning waveform was subjected to a series of waveshape tests.  The main objective being to discriminate between return stroke waveforms and waveforms from large amplitude cloud discharges.  We have implicity been assuming in our discussion that the lightning channel is vertically oriented.  This is a pretty reasonable assumption for cloud-to-ground discharges, especially at the time of peak field when the return stroke is close to the ground.  The unknown tilt of cloud discharge channels will add signficant errors to the estimate of bearing angle. 

The narrow positive bipolar pulse (NPBP) shown in the figure at right (together with a 1st return stroke waveform for comparison) is an as yet unidentified cloud discharge of some kind and produces particularly strong VHF radiation (the figure was adapted from J.C. Willett, J.C. Bailey, and E.P. Krider, "A Class of Unusual Lightning Electric Field Waveforms with Very Strong High-Frequency Radiation," J. Geophys. Res., 94, 16255-16267, 1989).

If the waveform passes the waveshape tests, the peak ampltitudes of the NS and the EW signals are measured.  At the time of peak signal, the return stroke is probably within about 100 m of the ground.  Estimating the bearing angle at this time is advantageous because you eliminate the effects of channel branches, the channel is usually fairly straight and vertical, and you're locating the point at which the stroke actually struck the ground.

Once bearing angle estimates are made at multiple DF sensor locations, you can then triangulate to locate the lightning strike point.  Errors in the bearing angle estimate of course lead to uncertainty in the lightning strike location.

Here we see the location determined using bearing angles from only 2 sensors (the minimum number required).  In the current NLDN network return strokes with a current of 25 kA would be detected by 6-8 sensors.  There are sophisticated methods for determining the optimal location with redundant data like that.

Large location errors can be present when a lightning strike is on or near a baseline between two sensors.





In some of the original direction finder networks the signal amplitudes were used to reduce the errors in locations on or near a baseline like this.  Now, of course, most strokes are detected at multiple stations.  Some of the other sensors would be off the baseline and would provide more accurate location information.  As we shall see the newer sensors also determine the time of arrival of the lightning signal at each sensor which provides additional independent location data.

One of the first uses of DF systems to locate lightning that might cause forest fires in Alaska and the western US.  For this application, relatively larger location errors (4 to 8 km) were acceptable.  Later as lightning location data began to be used by the power industry and insurance companies it became evident that sufficient location accuracy would not be possible using only magnetic direction finding unless sensors were on the order of 100 km apart.  Operation of a network covering the continental US with that kind of density would be too expensive (in the current network sensors are roughly 300 to 350 km apart and there are about 100 sensors covering the continental US).

A need for greater location accuracy eventually led to development of the so-called IMPACT sensor (improved accuracy from combined technology) that utilized both MDF and TOA.  The NLDN as configured in the late 1990s is shown below (from K.L. Cummins, M.J. Murphy, E.A. Bardo, W.L. Hiscox, R.B. Pyle and A.E. Pifer, "A Combined TOA/MDF Technology Upgrade of the U.S. National Lightning Detection Network," J. Geophys. Res., 103, 9035-9044, 1998). 



IMPACT sensors are shown with triangles, LPATS sensors with circles.  The LPATS sensors were from a lightning location network using just the TOA technique manufactured by Atmospheric Research Systems (ARSI) that had been installed in the US in the late 1980s.  The IMPACT sensor was designed and manufactured by Lightning Location & Protection, Inc. (LLP).

We will consider briefly the TOA technique below.  We assume that all three stations in the figure have either precisely synchronized clocks or accurate absolute timing (GPS timing).



There will be a constant difference in the time of arrival of a signal at Stations A and C from lightning striking anywhere on the blue curve (a hyperbola).


Similarly a hyperbola of constant TOA difference for Sensors B & C can be drawn.  The two curves intersect at two points.


You could resolve the location ambiguityusing magnetic bearing angles from the 3 sensors as shown above


Or you could draw another hyperbola - the curve of constant TOA difference for sensors A & B.

Or you could use all of the available location data.

The figure below shows an actual example of a discharge located using data from 5 stations in the NLDN (from the Cummins et al. article mentioned above).

Three IMPACT sensors (highlighted in brown, purple, and yellow) provide TOA information and bearing angle data.  Two LPATS sensors (at the centers of the blue and green circles) provided just TOA data.  Thus 8 independent pieces of information were used to locate this discharge.

A more recent network upgrade (see Cummins et al. in the Second Conference on Meteorological Applications of Lightning Data, Atlanta GA, 2006) was done in 2002 and all of the IMPACT and LPATS sensors were replaced with IMPACT ESP sensors.  The ESP (enhanced sensitivity and performance) sensors provide both MDF and TOA information.  The sensors are more sensitive and have faster processing times.  These improvements have increased the detection efficiency for low amplitude return strokes.  The new sensors also have the capability of detecting and locating some intracloud discharges.

Lightning location data from the NLDN is now being used in a wide variety of applications and it would seem appropriate to briefly discuss some recent attempts to measure the network detection efficiency and location accuracy.

Video ground truth data is probably the most common method of checking network performance.  Images of lightning strikes captured by two or more video cameras can be used to triangulate and determine strike locations just as is done with data from the MDF antennas.  The table below summarizes results collected from a small network of cameras operated in and around Albany, NY, in 1993, 1994, and 1995 (Idone et al. 1998a & 1998b; full citations are given at the end of this section).  Fast E field data were also recorded.  An upgrade of the NLDN, a switch from using just MDF to a network combining MDF and TOA techniques, was started and completed during the period of this experiment.
Albany, NY
Year
 Flash DE
 Stroke DE
 Location Accuracy
 Comments
1993
 67%
(517 flashes)
 ---
NLDN data for individual strokes
wasn't available at this time
1994
 86%
(893 flashes)
 67%
(2162 strokes)
 2.61 km
(median NLDN-video location separation)
1995
 72%
(433 flashes)
 47%
(1242 strokes)
435 m

 the number of NLDN sensors in the Albany
area was decreased slightly in 1995 at the
conclusion of the network upgrade

Video data does have some limitations.  First, the time resolution is somewhat limited.  A conventional video camera acquires 30 frames per second.  Each frame consists of two interlaced fields which can be displayed separately during playback.  Video is not be able to resolve two strokes that occur within the same video field, i.e. within a time of 16.7 ms.  And, actually, two strokes that occur on successive fields might be judged to be the same stroke if there is a long and luminous continuing current following the first stroke.  On the other hand a rebrightening of the lightning channel caused by an M component might be counted as separate stroke.  Some of these uncertainties can be resolved using a simultaneous record of fast E field changes.  It is practical to only cover a relatively small area with a video camera network.

The study above shows a slight improvement in DE after the network wide upgrade (72% vs 67%).  There was a marked increase in LA (435 m vs 2.61 km).  Locations and peak E field values were available for 92 strokes in the study.  The DE was shown to be a function of peak stroke current.  39 of 40 strokes with peak currents greater than 14 kA were detected by the NLDN.  Only 18% of strokes with peak currents between 6 and 10 kA were detected, and no strokes with peak currents below 6 kA were detected.

During the Albany experiment lightning was observed to strike a couple of tall buildings and a radio tower.  11 of these strokes were detected and located by the NLDN.  The mean difference between the known strike location and the NLDN location was 518 m.  10 strokes to a tall radio tower were also captured on video (1 of the strokes was detected by the NLDN).  The mean difference between the known strike location and the video location was 38 m; this provided a good check on the accuracy of the video locations.

In 2002-2003 the NLDN underwent another major upgrade wherein all of the IMPACT and LPATS sensors were replaced with IMPACT ESP (enhanced sensitivity and performance) sensors.  This was done partly to improved DE and LA near the boundaries of the network.  The table below summarizes measurements of DE made by Biagi et al. 2007 in southern Arizona, Texas, and Oklahoma.
Southern Arizona
Year
 Flash DE
 Stroke DE
 Corrected stroke DE
2003
 95%
(671 flashes)
 78%
(2290 strokes)
 70%
2004
 91%
(426 flashes)
 73%
(1330 strokes)
 66%
Overall
 93%
(1097 flashes)
 76%
(3620 strokes)
 68%


Texas and Oklahoma
Year
 Flash DE
 Stroke DE
 Corrected stroke DE
2003
 81%
(59 flashes)
 75%
(126 strokes)
2004
 94%
(308 flashes)
 87%
(756 strokes)
Overall
 92%
(367 flashes)
 86%
(882 strokes)
 77%


Data were collected with just a single video camera so the location accuracy was not measured.  Simultaneous fast time resolved measurements of fast E field and optical signals were also made.  These data were used to estimate that about 13% of the strokes were not resolved on the video because of the 16.7 ms video field integration time.  This was used to determine the corrected stroke DE values above.

Clearly the increased sensitivity of the IMPACT ESP sensors has improved the DE.  With this comes the possibility, however, that more low amplitude cloud discharge signals will be detected by the NLDN and mistakenly classified as cloud-to-ground (CG) discharges.  The data of Biagi et al. 2007 indicate this is a problem primarily for positive polarity signals.
Positive Polarity (TX and OK only)
peak current
 confirmed as CG discharges
Ipk ≤ 10 kA
 1.4 - 7%
10 kA < Ipk ≤ 20 kA 4.7 - 26%
20 kA < Ipk
 67 - 97%


Negative Polarity (S. AZ, TX, and OK)
peak current
 confirmed as CG discharges
Ipk ≤ 10 kA
 50 - 87%


As a final example we will give results from a study of NLDN performance in Florida using rocket triggered lightning (see Jerauld et al., 2005).
Year
 Flash DE
 Corrected Flash DE
 Stroke DE
 Location Accuracy
2001
 82%
(11 flashes)
 91%
(11 flashes)
 52%
(33 strokes)
 0.27 km
(median NLDL - known location separation)
2002
 86%
(14 flashes)
57%
(77 strokes)
 0.83 km
2003
 83%
(12 flashes)
 95%
(12 flashes)
 69%
(49 strokes)
 0.45 km
Overall
 84%
(37 flashes)
60%
(159 strokes)
 0.60 km

Detection efficiency was again found to depend on return stroke peak current.  Essentially 100% of strokes with a peak current greater than 30 kA were detected.  60% or 70% to about 90% of strokes with currents between 10 and 30 kA were detected.  Somewhat less than 30% of strokes with currents less than 10 kA were detected and no strokes with currents less than 5 kA were detected.

The corrected flash DE above attempts to account for the fact that triggered lightning flashes do not contain a first return like found in natural lightning.  We would expect first strokes to be detected more frequently than subsequent strokes because first strokes generally have higher peak currents.  This is discussed in somewhat more detail in Cummins et al. 2006.

Large (greater than 2 km) location errors were found for about 21% of the strokes in the study.  The majority (54%) of these had peak currents in the range of 5 to 10 kA.  About 55% of the cases with large location errors were located with only 2 sensors. 

A study involving triggered light also allows a comparison between estimates of peak stroke current derived from the NLDN data with direct measurements of current.  Mean peak current values are given in the table below.
Year
 Camp Blanding
 NLDN 
2001
 25.1 kA
 19.1 kA
2002
 17.0 kA
 15.7 kA
2003
 14.8 kA
 12.2 kA
Overall
 17.6 kA
 14.8 kA

Clearly the NLDN values understimate the true stroke current ampltitude.  This is also discussed in Cummins et al. 2006.  The source of this error is probably the attentuation correction that is made to the measured peak radiation field signals measured at the NLDN sensors sites before they can be used to estimate the peak current.  The attentuation of the fields due to propagation was probably being underestimated. 



List of references cited in this section

Biagi, C.J., K.L. Cummins, K.E. Kehoe, and E.P. Krider, "National Lightning Detection Network (NLDN) performance in southern Arizona, Texas, and Oklahoma in 2003-2004," J. Geophys. Res., 112, D05208, doi:10.1029/2006JD007341, 2007.

Cummins, K.L., J.A. Cramer, C.J. Biagi, E.P. Krider, J. Jerauld, M.A. Uman, V.A. Rakov, "The U.S. National Lightning Detection Network: Post-Upgrade Status, in the 2nd Conference on Meteorological Applications of Lightning Data, AMS Annual Meeting, Atlanta GA, 2006.

Idone, V.P., D.A. Davis, P.K. Moore, Y. Wang, R.W. Henderson, M. Ries, and P. Jamason, "Performance evaluation of the U.S. National Lightning Detection Network in eastern New York 1. Detection efficiency" J. Geophys. Res., 103, 9045-9055, 1998a.

Idone, V.P., D.A. Davis, P.K. Moore, Y. Wang, R.W. Henderson, M. Ries, and P. Jamason, "Performance evaluation of the U.S. National Lightning Detection Network in eastern New York 2. Location accuracy," J. Geophys. Res., 103, 9057-9069, 1998b.

Jerauld, J., V.A. Rakov, M.A. Uman, K.J. Rambo, D.M. Jordan, K.L. Cummins and J.A. Cramer, "An evaluation of the performance characteristics of the U.S. National Lightning Detection Network in Florida using rocket-triggered lightning," J. Geophys. Res., 110, D19106, doe:10.1029/2005jD005924, 2005.