Tuesday April 11, 2017

 In this lecture we will begin looking at some of the ground-based techniques used to locate lightning (we'll discuss satellite observations later in the course).  Cummins and Murphy (2009) provides a complete review of the history and current state of lightning location techniques and technology.  Ken Cummins also gave a keynote talk at the 2017 Eighth Conference on the Meteorological Application of Lightning Data in Seattle which is available online.  Nag et al. (2015) is another excellent and recent review of the topic.

We'll start today with the magnetic direction finding (MDF) and time of arrival (TOA) techniques currently being used in the ULF-LF frequency band in the National Lightning Detection Network (NLDN).  Click here to see a plot of lightning flash density for the continental U.S. for the period 2007-2016 based on NLDN data.

Radio frequency spectrum
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
(lightning also radiates visible light (wavelengths between 400 - 700 nm), X-rays (0.01 to 10 nm) and γ-rays (wavelengths < 10 pm) .


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 Hayenga and Warwick (1981).

Large current amplitude processes that propagate along long existing channels such as return strokes 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 approximately 400 Hz - 400 kHz (to just below the start of the AM radio band at 550 kHz) to locate lightning strikes to ground and more recently cloud discharges.   Signals at VLF and ULF frequencies can propagate 1000s of kilometers by "bouncing" back and forth between the earth's surface and the ionosphere.



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 un-ionized 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 that travel along an existing, conducting channel produce quasi continuous emissions that lasts 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 Cummins and Murphy (2009)).  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).

Magnetic direction finding
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 this figure 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 (current travels upward from the ground) 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 Θ 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.  There'll also be a signal induced in the EW antenna.

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 (upper waveform in blue) and EW signals (lower waveform in each pair and in green) produced by lightning strikes at various locations are shown below.


The ratio of the EW and NS signal amplitudes gives you the direction to the discharge.  The square root of the sum of the squares of the two signals provides the B field amplitude.

Once the distance to the discharge is determined, the B field amplitude (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 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 are shown below (both photos from Krider et al., 1980).


The crossed loop magnetic field antenna used in the original lightning locating system in interior Alaska (late 1970s).  An early application of lightning locations was was detection of fires caused by lightning.
 A photograph of the next generation magnetic field antenna.  The accompanying electric field antenna can be seen at left edge of the photograph.



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 wave shape tests.  The main objective being to discriminate between return stroke waveforms and waveforms from large amplitude cloud discharges.  We have 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 significant 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 a not yet well understood cloud discharge of some kind and produces particularly strong VHF radiation (the figure was adapted from Willett et al., 1989)

If the waveform passes the wave shape tests, the peak amplitudes 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 sensors in the present day network also determine the time of arrival of the lightning signal at each sensor which provides additional independent location data.

The US National Lightning Detection Network
One of the first uses of DF systems was to locate lightning that might cause forest fires in remote parts of 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 just over 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 (Cummins et al., 1998).



A total of 106 sensors is shown. 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). 

Time of arrival technique used to locate lightning
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 ambiguity by using magnetic bearing angles from the 3 sensors as shown above.  Note that drawing the third hyperbola, the curve of constant TOA difference for sensors A & B would not resolve the ambiguity.  This is because information from stations A and B was already used in drawing the two initial (blue and green) hyperbolas. 

The figure below shows an actual example of a discharge located using data from 5 stations in the NLDN (from the Cummins et al. (1998) article mentioned above).

Three IMPACT sensors (Xs in the figure) provide TOA information and bearing angle data.  Two LPATS sensors (Os 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.

Another network upgrade was done in 2002 and all of the IMPACT and LPATS sensors were replaced with IMPACT ESP sensors (see Cummins et al., (2006)).  The ESP (enhanced sensitivity and performance) sensors provide both MDF and TOA information.  The sensors were more sensitive and had faster processing times.  These improvements increased the detection efficiency for low amplitude return strokes.  The new sensors also had the capability of detecting and locating some large amplitude intracloud discharges.

Ground truth: determining NLDN detection efficiency and location accuracy
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 (DE) and location accuracy (LA).  With one exception, we'll just consider validation experiments that followed the 2002-2003 upgrade when all of the IMPACT and LPATS sensors were replaced with IMPACT ESP (enhanced sensitivity and performance) sensors.  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.

These experiments showed that 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 was 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%


Triggered lightning is another way of validating NLDN performance.  This has the advantage that NLDN estimates of peak return stroke current can be compared with current measurements made at the triggering site.  Here we'll show results obtained before and after network upgrades made in 2002-2003, 2010-2012 and 2013 to see how detection efficiency (DE) and location accuracy (LA) have improved.

Jerauld et al. (2005) data (lightning triggered in 2001-2003)

 Flash DE
 Stroke DE
 Location Accuracy
Overall
 84%
(31 of 37 flashes)
 60%
(95 of 159 strokes)
 600 m
median (NLDN - known location) difference

2002-2003 upgrade
(all of the IMPACT & LPATS sensors were replaced with IMPACT ESP sensors)
Nag et al. (2011) data (lightning triggered in 2004-2009)

 Flash DE
 Stroke DE
 Location Accuracy
Overall
 92% (34 of 37 flashes)
 76% (105 of 139 strokes) 308 m


2010-2012 upgrade
(all of the IMPACT ESP sensors were gradually replaced with fully digital LS7001 sensors)

Mallick et al. (2012) (lightning triggered in 2010 & 2011)

 Flash DE
 Stroke DE
 Location Accuracy
Overall
 100% (23 of 23 flashes)
 72% (64 of 89 strokes)
 436 m


April - August 2013 upgrade
(LS7001 sensors replaced with LS7002 sensors)
Mallick et al. (2014) (lightning triggered in 2012 & 2013)

 Flash DE
 Stroke DE
 Location accuracy
2012
 95% (18 of 19 flashes)
 76% (77 of 101 strokes)
 258 m
2013
 100% (12 of 12 flashes)
 76% (47 of 62 strokes)
 173 m


NLDN locations of cloud discharges
The NLDN which originally just used MDF to locate lightning purposely sought to identify and exclude cloud discharges.  This was because non vertical channels would introduce bearing angle errors.  At some point in the early 2000s a decision was made to begin to locate cloud discharges.

Using triggered lightning to validate NLDN peak current estimates
Signal amplitudes measured by the sensors in the NLDN are also used to make estimates of lightning return stroke peak currents.  Those estimates make use of the simple transmission line model expression that relates peak current I and the peak amplitude of the electric and magnetic radiation fields (both E and B fields are measured by the sensors in the NLDN).  Triggered lightning return strokes closely resemble the subsequent return strokes in natural lightning.  Most of the lightning triggered at the International Center for Lightning Research and Testing (ICLRT) at Camp Blanding in north Florida is detected and located by the National Lightning Detection Network.  This data set can be used to evaluate the accuracy of the peak current estimates made by the NLDN (at least the SE portion of the network). 


A map showing the locations of stations in the National Lightning Detection Network near the International Center for Lightning Research and Testing at Camp Blanding, Florida.

The transmission line model relationship between peak current, Ipk, and peak values of the electric and magnetic radiation fields at a distance D from the discharge are shown below:



The constant μo is referred to as the permeability of free space, the vacuum permeability, and the magnetic constant.  μo and εo (the permittivity of free space) are related in the following way




The measured B field values are first range normalized to 100 km using an inverse distance relationship.  Then the amplitude is corrected for attenuation during propagation.

A measured field amplitude of 1.5 x 10-8 W/m2 at a range of 200 km would be multiplied by 2 to range normalize the amplitude to 100 km.  The value would then be multiplied by a factor of 1.095 to account for propagation attenuation.  The range normalized value of B is then used in the transmission line model expression to estimate the peak current amplitude.

A total of 351 return strokes were triggered at Camp Blanding during the 2004-2013 time period.  The distribution of peak current values is shown below at left, the geometric mean was 11.8 kA.  The average current was 14 kA, the largest and smallest currents measured were 44.6 kA and 2.0 kA respectively (strokes with currents less than about 5 kA are not detected by the NLDN).
Distribution of measured peak currents
in rocket-triggered lightning
 Comparison between measured peak currents
and NLDN estimates of peak currents


The plot at right above compares NLDN estimates of peak currents with peak currents measured at the ICLRT facility.  

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.

C.O. Hayenga and J. W. Warwick, "Two-Dimensional Interferometric Positions of VHF Lightning Sources", J. Geophys. Res., 86, 7451-7462, 1981

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.

Cummins, K.L. 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. EMC, 51, 499-518, 2009.

Cummins, K.L., "Lightning Locating Systems: History, Methods, and their Roles in Meteorological Applications," presented at the Eighth Conf. on the Meterol. Application of Lightning Data, Amer. Meterol. Soc., Seattle, Jan. 2017.

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.

Krider, E.P., R.C. Noggle, A.E. Pifer, and D.L. Vance, "Lightning Direction-Finding Systems for Forest Fire Detection," , Bull. Am. Meteorol. Soc., 61, 980-986, 1980

Mallick, S., V.A. Rakov, J.D. Hill, T. Ngin, W.R. Gamerota, D.M. Jordan, R.C. Olsen III, M.A. Uman, "The NLDN Performance Characteristics: An Update," 22nd Intl Lightning Detection Conf., Broomfield, CO, April, 2012.

Mallick, S., V.A. Rakov, T. Ngin, W.R. Gamerota, J.T. Pilkey, J.D. Hill, M.A. Uman, D.M. Jordan, "An Update on the Performance Characteristics of the NLDN," 23rd Intl Lightning Detection Conf., Tucson, AZ, 2014.

Nag, A. S. Mallick, V.A. Rakov, J.S. Howard, C.J. Biagi, J.D. Hill, NM.A. Uman, D.M. Jordan, K.J. Rambo, J.E. Jerauld, B.A. DeCarlo, K.L. Cummins and J.A. Cramer, "Evaluation of U.S. National Lightning Detection Network performance characteristics using rocket-triggered lightning data acquired in 2004-2009", J. Geophys. Res., 116, 2011, doi:10.1029/2010JD014929.

Nag, A., M.J. Murphy, W. Schulz and K. Cummins, "Lightning locating systems: Insights on characteristics and validation techniques," Earth and Space Science, 2,65-93, 2015. doi:10:1002/2014EA000051.

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).